Question 1

Solve.
-$-2 x=-16$

Accepted Answer

A)  -14 
B)  14 
C)  8 
D)  2 
A)  -14 
B)  14 
C)  8 
D)  2 C

Question 2

Solve.
-$10.6=-18.6-\mathrm{n}$

Accepted Answer

A)  29.2 
B)  8 
C)  -8 
D)  -29.2 
A)  29.2 
B)  8 
C)  -8 
D)  -29.2 D

Question 3

Provide an appropriate response.
-Consider the equation $7 x=3 x$. If you divide both sides by $x$ you get $7=3$. Is there $a$ solution? If yes, how do you get it, and why didn't the given method work?

Accepted Answer

The solution is x = 0. Subtract 3x from both sides, then divide both sides by 4. When dividing both sides by x you don't find the solution because you cannot divide by zero.

Question 4

Solve
-$2=8 m-3 m-2$

Accepted Answer

A)  -1 
B)  $\frac{1}{2}$ 
C)  0 
D)  $\frac{4}{5}$ 
A)  -1 
B)  $\frac{1}{2}$ 
C)  0 
D)  $\frac{4}{5}$

Question 5

Write an equation to find the number. Solve.
-Three times the sum of a number and 7 equals twice the number.

Accepted Answer

A)  $3 x+7=2 x ; x=7$ 
B)  $3 x+7=2 x ; x=-7$ 
C)  $3(x+7)=2 x ; x=21$ 
D)  $3(x+7)=2 x ; x=-21$ 
A)  $3 x+7=2 x ; x=7$ 
B)  $3 x+7=2 x ; x=-7$ 
C)  $3(x+7)=2 x ; x=21$ 
D)  $3(x+7)=2 x ; x=-21$

Question 6

Solve.
-$-12=\frac{b}{5}$

Accepted Answer

A)  $b=60$ 
B)  $b=-60$ 
C)  $b=-2 \frac{2}{5}$ 
D)  $b=17$ 
A)  $b=60$ 
B)  $b=-60$ 
C)  $b=-2 \frac{2}{5}$ 
D)  $b=17$

Question 7

Solve the equation
-$\frac{1}{2}(x+3)=3$

Accepted Answer

A)  18 
B)  3 
C)  9 
D)  0 
A)  18 
B)  3 
C)  9 
D)  0

Question 8

Use an equation to solve the problem.
-The height of the tallest building in Anne's home town is $617 \mathrm{ft}$, which is about $233 \mathrm{ft}$ taller than the tallest building in Laurie's home town. What is the height of the tallest building in Laurie's home town?

Accepted Answer

A)  $384 \mathrm{ft}$ 
B)  $850 \mathrm{ft}$ 
C)  $497 \mathrm{ft}$ 
D)  $233 \mathrm{ft}$ 
A)  $384 \mathrm{ft}$ 
B)  $850 \mathrm{ft}$ 
C)  $497 \mathrm{ft}$ 
D)  $233 \mathrm{ft}$

Question 9

Provide an appropriate response.
-When solving the equation $4 x+7=5$, why is 7 subtracted from both sides first instead of dividing both sides by 4 first?

Accepted Answer

When solving an algebraic equa

Question 10

Translate the stated rule or relationship to a formula.
-The gas mileage, $\mathrm{e}$, for a car is calculated by dividing the number of miles driven, $\mathrm{m}$, by the number of gallons, $\mathrm{g}$, of gas used.

Accepted Answer

A)  $\mathrm{e}=\mathrm{m}+\mathrm{g}$ 
B)  $\mathrm{e}=\frac{\mathrm{m}}{\mathrm{g}}$ 
C)  $\mathrm{e}=\frac{\mathrm{g}}{\mathrm{m}}$ 
D)  $\mathrm{e}=\mathrm{mg}$ 
A)  $\mathrm{e}=\mathrm{m}+\mathrm{g}$ 
B)  $\mathrm{e}=\frac{\mathrm{m}}{\mathrm{g}}$ 
C)  $\mathrm{e}=\frac{\mathrm{g}}{\mathrm{m}}$ 
D)  $\mathrm{e}=\mathrm{mg}$

Question 11

Solve.
-$22-y=5$

Accepted Answer

A)  $y=-17$ 
B)  $y=17$ 
C)  $y=27$ 
D)  $y=-27$ 
A)  $y=-17$ 
B)  $y=17$ 
C)  $y=27$ 
D)  $y=-27$

Question 12

Write an equation for the word problem. Then solve and check.
-During a sale, the price of a jacket was reduced by $\frac{1}{3}$. With a coupon, an additional $\$ 10$ was taken off at the cash register. If the final price of the jacket was $\$ 50$, what was the original price?

Accepted Answer

A)  $x-\frac{1}{3}=50-10 ; \$ 60.00$ 
B)  $\frac{1}{3} x-10=50 ; \$ 180$ 
C)  $x-\frac{1}{3} x-10=50 ; \$ 90$ 
D)  $x-\frac{1}{3} x=50 ; \$ 75.00$ 
A)  $x-\frac{1}{3}=50-10 ; \$ 60.00$ 
B)  $\frac{1}{3} x-10=50 ; \$ 180$ 
C)  $x-\frac{1}{3} x-10=50 ; \$ 90$ 
D)  $x-\frac{1}{3} x=50 ; \$ 75.00$

Question 13

Simplify.
-$\frac{3}{5} m+\frac{3}{25} m$

Accepted Answer

A)  $\frac{18}{25} m^{2}$ 
B)  $\frac{91}{125} \mathrm{~m}^{2}$ 
C)  $\frac{91}{125} \mathrm{~m}$ 
D)  $\frac{18}{25} \mathrm{~m}$ 
A)  $\frac{18}{25} m^{2}$ 
B)  $\frac{91}{125} \mathrm{~m}^{2}$ 
C)  $\frac{91}{125} \mathrm{~m}$ 
D)  $\frac{18}{25} \mathrm{~m}$

Question 14

Solve the equation. Round the solution to the nearest tenth.
-$0.814 \mathrm{~s}=-4.257 \mathrm{~s}+4.94 \mathrm{~s}-5.917$

Accepted Answer

A)  -45.2 
B)  6 
C)  0 
D)  -0.8 
A)  -45.2 
B)  6 
C)  0 
D)  -0.8

Question 15

Solve.
-$-4 \mathrm{a}=28$

Accepted Answer

A)  1 
B)  -7 
C)  -32 
D)  32 
A)  1 
B)  -7 
C)  -32 
D)  32

Question 16

Solve.
-$\frac{1}{3} x=14$

Accepted Answer

A)  17 
B)  28 
C)  42 
D)  39 
A)  17 
B)  28 
C)  42 
D)  39

Question 17

Solve the equation.
-$2 r+3=21$

Accepted Answer

A)  7 
B)  16 
C)  9 
D)  20 
A)  7 
B)  16 
C)  9 
D)  20

Question 18

Use an equation to solve the problem.
-Junior high classes of 35 students each met in the cafeteria to take achievement tests. If exactly 5 students sat at each table and 28 tables were used, how many classes took the tests?

Accepted Answer

A)  17 classes 
B)  4 classes 
C)  7 classes 
D)  6 classes 
A)  17 classes 
B)  4 classes 
C)  7 classes 
D)  6 classes

Question 19

Solve the equation.
-$44=27-8 \mathrm{~s}$

Accepted Answer

A)  $-\frac{17}{8}$ 
B)  35 
C)  $\frac{17}{8}$ 
D)  $-\frac{71}{8}$ 
A)  $-\frac{17}{8}$ 
B)  35 
C)  $\frac{17}{8}$ 
D)  $-\frac{71}{8}$

Question 20

Solve the equation.
-$22+\frac{m}{5}=-18$

Accepted Answer

A)  -112 
B)  200 
C)  -200 
D)  -8 
A)  -112 
B)  200 
C)  -200 
D)  -8

Solve. - $-2 x=-16$

Solve. - $10.6=-18.6-\mathrm{n}$

Provide an appropriate response. -Consider the equation $7 x=3 x$ . If you divide both sides by $x$ you get $7=3$ . Is there $a$ solution? If yes, how do you get it, and why didn't the given method work?

Solve - $2=8 m-3 m-2$

Write an equation to find the number. Solve. -Three times the sum of a number and 7 equals twice the number.

Solve. - $-12=\frac{b}{5}$

Solve the equation - $\frac{1}{2}(x+3)=3$

Use an equation to solve the problem. -The height of the tallest building in Anne's home town is $617 \mathrm{ft}$ , which is about $233 \mathrm{ft}$ taller than the tallest building in Laurie's home town. What is the height of the tallest building in Laurie's home town?

Provide an appropriate response. -When solving the equation $4 x+7=5$ , why is 7 subtracted from both sides first instead of dividing both sides by 4 first?

Translate the stated rule or relationship to a formula. -The gas mileage, $\mathrm{e}$ , for a car is calculated by dividing the number of miles driven, $\mathrm{m}$ , by the number of gallons, $\mathrm{g}$ , of gas used.

Solve. - $22-y=5$

Write an equation for the word problem. Then solve and check. -During a sale, the price of a jacket was reduced by $\frac{1}{3}$ . With a coupon, an additional $\$ 10$ was taken off at the cash register. If the final price of the jacket was $\$ 50$ , what was the original price?

Simplify. - $\frac{3}{5} m+\frac{3}{25} m$

Solve the equation. Round the solution to the nearest tenth. - $0.814 \mathrm{~s}=-4.257 \mathrm{~s}+4.94 \mathrm{~s}-5.917$

Solve. - $-4 \mathrm{a}=28$

Solve. - $\frac{1}{3} x=14$

Solve the equation. - $2 r+3=21$

Use an equation to solve the problem. -Junior high classes of 35 students each met in the cafeteria to take achievement tests. If exactly 5 students sat at each table and 28 tables were used, how many classes took the tests?

Solve the equation. - $44=27-8 \mathrm{~s}$

Solve the equation. - $22+\frac{m}{5}=-18$

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Exam 9: More on Algebra

Solve. - −2x=−16-2 x=-16−2x=−16

Solve. - 10.6=−18.6−n10.6=-18.6-\mathrm{n}10.6=−18.6−n

Provide an appropriate response. -Consider the equation 7x=3x7 x=3 x7x=3x . If you divide both sides by xxx you get 7=37=37=3 . Is there aaa solution? If yes, how do you get it, and why didn't the given method work?

Solve - 2=8m−3m−22=8 m-3 m-22=8m−3m−2

Write an equation to find the number. Solve. -Three times the sum of a number and 7 equals twice the number.

Solve. - −12=b5-12=\frac{b}{5}−12=5b​

Solve the equation - 12(x+3)=3\frac{1}{2}(x+3)=321​(x+3)=3

Use an equation to solve the problem. -The height of the tallest building in Anne's home town is 617ft617 \mathrm{ft}617ft , which is about 233ft233 \mathrm{ft}233ft taller than the tallest building in Laurie's home town. What is the height of the tallest building in Laurie's home town?

Provide an appropriate response. -When solving the equation 4x+7=54 x+7=54x+7=5 , why is 7 subtracted from both sides first instead of dividing both sides by 4 first?

Translate the stated rule or relationship to a formula. -The gas mileage, e\mathrm{e}e , for a car is calculated by dividing the number of miles driven, m\mathrm{m}m , by the number of gallons, g\mathrm{g}g , of gas used.

Solve. - 22−y=522-y=522−y=5

Write an equation for the word problem. Then solve and check. -During a sale, the price of a jacket was reduced by 13\frac{1}{3}31​ . With a coupon, an additional $10\$ 10$10 was taken off at the cash register. If the final price of the jacket was $50\$ 50$50 , what was the original price?

Simplify. - 35m+325m\frac{3}{5} m+\frac{3}{25} m53​m+253​m

Solve the equation. Round the solution to the nearest tenth. - 0.814 s=−4.257 s+4.94 s−5.9170.814 \mathrm{~s}=-4.257 \mathrm{~s}+4.94 \mathrm{~s}-5.9170.814 s=−4.257 s+4.94 s−5.917

Solve. - −4a=28-4 \mathrm{a}=28−4a=28

Solve. - 13x=14\frac{1}{3} x=1431​x=14

Solve the equation. - 2r+3=212 r+3=212r+3=21