Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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Solve the equation.
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1.
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–49 = x – 50
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2.
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v –  = 
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3.
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14 = t + 7
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4.
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d + 0.7 = 0.9
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5.
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a. |  | b. | –14 | c. | 40 | d. | –40 |
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6.
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 x = 27
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7.
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9d = –54
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8.
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9.
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 x + 5 = 8
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10.
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11 = –d + 15
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11.
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12.
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37 – 18 + 8w = 67
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13.
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3(y + 6) = 30
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14.
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a. | –31 | b. |  | c. | –50 | d. | –35 |
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15.
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4.9x + 4.4 = 19.1
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16.
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17.
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18.
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a. | 28 | b. |  | c. |  | d. | 3 |
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19.
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20.
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5x – 5 = 3x – 9
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21.
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8d – 4d – 6d – 8 = 2d
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22.
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Two angles are complementary if the sum of their measures is  . 
and  are complementary. The measure of  is  . Write and solve an
equation to find the measure of  .
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23.
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The triangle below is isosceles with congruent sides  and  . Find the
value of x. 
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24.
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A gardener measures the tallest of his prize-winning sunflowers and finds that
the height is 60 in. The sunflower was 52 in. tall the last time the gardener measured it.
Write and solve an equation to find how many inches the sunflower grew.
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25.
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Sirus wrote a check for $67. He subtracted that amount from his account balance
and found that the balance was $329 after writing the check. Write and solve an equation to find his
balance before writing the check.
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26.
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You are driving to visit a friend in another state who lives 440 miles away. You
are driving 55 miles per hour and have already driven 275 miles. Write and solve an equation to find
how much longer in hours you must drive to reach your destination.
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27.
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A customer went to a garden shop and bought some potting soil for $17.50 and 4
shrubs. The total bill was $53.50. Write and solve an equation to find the price of each
shrub.
a. | 4p + $17.50 = $53.50; p = $9.00 | c. | 4p + 17.5p = $53.50;
p = $2.49 | b. | 4(p + $17.50) = $53.50; p = $4.00 | d. | 4p + $17.50 = $53.50; p =
$11.25 |
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28.
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Steven wants to buy a $565 bicycle. Steven has no money saved, but will be able
to deposit $30 into a savings account when he receives his paycheck each Friday. However, before
Steven can buy the bike, he must give his sister $65 that he owes her. For how many weeks will Steven
need to deposit money into his savings account before he can pay back his sister and buy the
bike?
a. | 25 weeks | b. | 19 weeks | c. | 22 weeks | d. | 21
weeks |
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29.
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Which properties of equality justify steps c and f?  a. | Subtraction Property of Equality; Multiplication Property of
Equality | b. | Addition Property of Equality; Division Property of Equality | c. | Addition Property of
Equality; Subtraction Property of Equality | d. | Multiplication Property of Equality; Division
Property of Equality |
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30.
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Find the value of y. 
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31.
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John and 2 friends are going out for pizza for lunch. They split one pizza and 3
large drinks. The pizza cost $14.00. After using a $7.00 gift certificate, they spend a total of
$12.10. Write an equation to model this situation, and find the cost of one large drink.
a. | 3d + $14.00 – $7.00 = $12.10; $1.70 | b. | 2d + $14.00
– $7.00 = $12.10; $2.55 | c. | 3d – $14.00 + $7.00 = $12.10;
$9.55 | d. | 3d + $14.00 – $7.00 = $12.10; $1.90 |
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32.
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Find the measure of  . (Hint: The sum of the measures of the angles in a
triangle is  .) 
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33.
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a. Find the value of a. b. Find the value of the marked
angles. 
a. | 22; 100º | b. | 19; 88º | c. | 20; 92º | d. | 24;
108º |
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34.
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A camera manufacturer spends $2,100 each day for overhead expenses plus $9 per
camera for labor and materials. The cameras sell for $14 each. a. How many cameras must the company sell in one day to equal its
daily costs?
b. If the manufacturer can increase production by 50 cameras per day, what
would their daily profit be? a. | 420; $250 | b. | 480; $550 | c. | 380;
$50 | d. | 150; $1100 |
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35.
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A copy center offers its customers two different pricing plans for black and
white photocopies of 8.5 in. by 11 in. pages. Customers can either pay $.08 per page or can
pay $7.50 for a discount card that lowers the cost to $.05 per page. Write and solve an equation to
find the number of photocopies for which the cost of each plan is the same.
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36.
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Find the value of each variable. 
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37.
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Which equation is an identity?
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38.
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The length of a rectangle is 5 centimeters less than twice its width. The
perimeter of the rectangle is 26 cm. What are the dimensions of the rectangle?
a. | length = 5 cm; width = 5 cm | c. | length = 6 cm; width = 7
cm | b. | length = 7 cm; width = 6 cm | d. | length = 4 cm; width = 9 cm |
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39.
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Peter is reading a 193-page book. He has read three pages more than one fourth
of the number of pages he hasn’t yet read. a. How many
pages has he not yet read?
b. Estimate how many days it will take Peter to finish the book
if he reads about 8 pages per day. a. | 144; about 18 days | c. | 152; about 19 days | b. | 147; about 18 days | d. | 141; about 18
days |
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40.
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The sum of two consecutive integers is 59. Write an equation that models this
situation and find the values of the two integers.
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41.
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The sum of four consecutive odd integers is  . Write an equation to
model this situation, and find the values of the four integers.
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42.
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Carlos and Maria drove a total of 258 miles in 5 hours. Carlos drove the first
part of the trip and averaged 53 miles per hour. Maria drove the remainder of the trip and averaged
51 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest
tenth if necessary.
a. | 3.5 hours | b. | 2.5 hours | c. | 1.8 hours | d. | 1.5
hours |
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43.
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Runner A crosses the starting line of a marathon and runs at an average pace of
5.6 miles per hour. Half an hour later, Runner B crosses the starting line and runs at an average
rate of 6.4 miles per hour. If the length of the marathon is 26.2 miles, which runner will finish
ahead of the other? Explain.
a. | Runner B; Runner B will catch up to Runner A 4 hours after Runner A crosses the
starting line. | b. | Runner B; Runner B will pass Runner A and finish more than half an hour ahead of
Runner A. | c. | Runner B; Runner B will catch up to runner A 3.5 hours after Runner A crosses the
starting line. | d. | Runner A; Runner B will not be able to catch Runner A in the time it takes Runner A
to complete the 26.2 mile course. |
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44.
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At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass
each other on a bicycle path.The bicyclist heading north is riding 6 km/hour faster than the
bicyclist heading south. At 10:15, they are 42.5 km apart. Find the two bicyclists’
rates.
a. | northbound bicyclist = 20 km/h; southbound bicyclist = 14 km/h | b. | northbound bicyclist
= 23 km/h; southbound bicyclist = 17 km/h | c. | northbound bicyclist = 18 km/h; southbound
bicyclist = 11 km/h | d. | northbound bicyclist = 20 km/h; southbound
bicyclist = 13 km/h |
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45.
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Toni rows a boat 4.5 km/h upstream and then turns around and rows 5.5 km/h back
downstream to her starting point. If her total rowing time is 48 min, for how long does she row
upstream? Express your answer to the nearest minute.
a. | about 44 min | c. | about 24 min | b. | about 26 min | d. | about 30 min |
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46.
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Solve the formula for area of a trapezoid  for
b1. a. | b1 =  | c. | b1 =  | b. | b1 =  | d. | b1 =  |
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47.
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The formula for converting degrees Celsius ( C) to degrees Fahrenheit
( F) is  . Solve the formula for degrees Celsius ( C). Then
find the temperature in degrees Celsius ( C) when the temperature in degrees Fahrenheit
( F) is –4. a. | –20° C | b. | –29° C | c. | –14° C | d. | –7°
C |
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48.
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Solve the equation for a. 
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Solve the equation for the given variable.
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49.
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 ; w
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50.
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 ; x
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51.
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 ; z
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52.
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 ; t
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53.
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Over the first five years of owning her car, Gina drove about 12,700 miles the
first year, 15,478 miles the second year, 12,675 the third year, 11,850 the fourth year, and
13,075 the fifth year. a. Find the mean, median, and mode of
this data.
b. Explain which measure of central tendency will best predict how many miles
Gina will drive in the sixth year. a. | mean = 12,700; median = 13,156; no mode; the mean is the best choice because it is
representative of the entire data set. | b. | mean = 13,156; median = 12,700; mode = 3,628;
the median is the best choice because it is not skewed by the high outlier. | c. | mean = 13,156;
median = 12,700; no mode; the mean is the best choice because it is representative of the entire data
set. | d. | mean = 13,156; median = 12,700; no mode; the median is the best choice because it is
not skewed by the high outlier. |
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54.
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Angela’s average for six math tests is 87. On her first four tests she had
scores of 93, 87, 82, and 86. On her last test, she scored 4 points lower than she did on her fifth
test. What scores did Angela receive on her fifth and sixth tests?
a. | fifth test = 85; sixth test = 89 | c. | fifth test = 90; sixth test =
86 | b. | fifth test = 85; sixth test = 81 | d. | fifth test = 89; sixth test =
85 |
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55.
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Your math teacher allows you to choose the most favorable measure of central
tendency of your test scores to determine your grade for the term. On six tests you earn scores of
89, 81, 85, 82, 89, and 89. What is your grade to the nearest whole number, and which measure of
central tendency should you choose?
a. | 87; the median | b. | 89; the mean | c. | 91; the mode | d. | 89; the
mode |
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Write and solve an equation to find the value of the variable.
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56.
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104, 137, 154, 131, x; mean = 130
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57.
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5.2, 8.3, 8.5, 7.7, 7.8, y; mean = 7.1
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58.
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A carpenter cut four lengths of wood. The lengths were  in., 
in.,  in., and z in. If the mean of the lengths is  in., what was the length
of the fourth piece of wood the carpenter cut?
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Find the range.
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59.
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3 –9 7 –1
5 –4 2
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60.
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4.7 6.3 5.4 3.2 4.9
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61.
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Find the mean and range. 18  23  10  39  22  17  16  15 a. | mean = 20; range = 29 | c. | mean = 21.9; range = 29 | b. | mean = 20; range =
32 | d. | mean = 18.1; range =
28 |
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62.
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Make a stem-and-leaf plot for the following set of data.
1.1, 1.3, 1.8, 2.2,
2.6, 2.8, 3.1, 3.8
a. | 
1 ½ 1 =
1.1 | c. | 
1 ½ 0.1 =
1.01
| b. | 
1 ½ 1 =
1.1
| d. | 
1 ½ 8 = 1.8 |
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63.
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Determine whether the statement is sometimes, always or never
true. If ax + b – 4 = b and  then
 . a. | always | b. | sometimes | c. | never |
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64.
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The perimeter of the rectangle is 24 cm. Find the value of x.  a. | 3 | b. | 12 | c. |  | d. | 18 |
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65.
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Determine whether the following statement is sometimes, always, or
never true.
If two sets of data have the same range and the same mean then they have the
same mode.
a. | sometimes | b. | always | c. | never |
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Short Answer
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66.
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Justify each step. 
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67.
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Bob and Nancy recorded their last ten rounds of golf scores in the stem-and-leaf
plot below. Use measures of central tendency to justify your answers. a. Who is the better golfer? (A player with a lower score beats a
player with a higher score.)
b. Is one golfer more consistent than the other?
Explain. Nancy | Stem | Bob | 9 8
7 | 7 | 5 9 | 8 6 5 5 2 | 8 | 3 3 3 8 9 | 1 0 | 9 | 0 3 7 | | | |
7 ½5 = 75
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68.
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A class writes the equation n + n + 1 + n + 2 = 87 to solve
the following problem.
The sum of 3 consecutive odd integers
is 87. Find the three integers.
What error did they make?
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Essay
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69.
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Solve the equation. Justify each step.
–10x + 5 =
–15
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70.
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Determine whether the following statement is sometimes, always, or
never true. Show your work.
Every 2-digit number ending in 5 can be written as the sum
of three consecutive integers.
(Hint: Try 15 and 25.)
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71.
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The length of a rectangle is 8 cm more than 3 times its width. The perimeter of
the rectangle is 64 cm.
a. What are the dimensions of the rectangle? Show your
work.
b. What is the area of the rectangle? Show your work.
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72.
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The formula for converting temperature in degrees Fahrenheit ( F) to
degrees Celsius ( C) is  . For outdoor temperatures in the United States, here is
an easy way to estimate the temperature in degrees Fahrenheit ( F) when you know the
temperature in degrees Celsius ( C): Double the number of degrees Celsius ( C) and add
30. a. Does this method provide a reasonable estimate of
degrees Fahrenheit (F)? Explain
( hint: Solve
 for F.) b. Use this method to
estimate the temperature in degrees Fahrenheit (F) when it is 25°C outside. Show your
work.
c. How far is the estimate from the actual Fahrenheit temperature?
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Other
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73.
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Explain the error in the student’s work. 
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74.
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Explain why this statement is always true.
If x is an odd integer,
then the median of x, x + 2, x + 6, and x + 10 is an odd number.
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75.
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The standard method for solving an equation like  is to use the
Subtraction Property of Equality and then the Division Property of Equality. It is possible to solve
the equation using the properties in the reverse order. Explain why the standard method is
better.
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