Question 1

Solve the equation.
-$\frac { 2 x } { 5 } - \frac { x } { 3 }$ = 5

Accepted Answer

A) 150 
B) 75 
C) -75 
D) -150 
A) 150 
B) 75 
C) -75 
D) -150

Question 2

Solve.
-When making a long distance call from a certain pay phone, the first three minutes of a call cost $2.75. After that, each additional minute or portion of a minute of that call costs $0.40. Use an inequality to find the
Maximum number of minutes one can call long distance for $3.55.

Accepted Answer

A) at most 2 minutes 
B) at most 9 minutes 
C) at most 5 minutes 
D) at most 1 minutes 
A) at most 2 minutes 
B) at most 9 minutes 
C) at most 5 minutes 
D) at most 1 minutes

Question 3

Solve.
-The manager of a coffee shop has one type of coffee that sells for $6 per pound and another type that sells for $12 per pound. The manager wishes to mix 100 pounds of the $12 coffee to get a mixture that will sell for $10
Per pound. How many pounds of the $6 coffee should be used?

Accepted Answer

A) 75 pounds 
B) 50 pounds 
C) 150 pounds 
D) 25 pounds 
A) 75 pounds 
B) 50 pounds 
C) 150 pounds 
D) 25 pounds

Question 4

Solve. Round to the nearest hundredth, if necessary.
-20 is 9% of what number?

Accepted Answer

A) 222.22 
B) 22.22 
C) 2222.2 
D) 180 
A) 222.22 
B) 22.22 
C) 2222.2 
D) 180

Question 5

Solve the equation.
-7(x + 4)+ 58 = 9x - 2(x - 7)

Accepted Answer

A) 72 
B) no solution 
C) all real numbers 
D) 44 
A) 72 
B) no solution 
C) all real numbers 
D) 44

Question 6

Solve.
-The sum of four times a number and three is the same as the difference of twice the number and eleven. Find the number.

Accepted Answer

A) 7 
B) -17 
C) -7 
D) 4 
A) 7 
B) -17 
C) -7 
D) 4

Question 7

Solve the equation.
-$\frac { 1 } { 5 }$ + x = 3

Accepted Answer

A) 14 
B)  $\frac { 14 } { 5 }$ 
C)  $\frac { 16 } { 5 }$ 
D)  $\frac { 2 } { 5 }$ 
A) 14 
B)  $\frac { 14 } { 5 }$ 
C)  $\frac { 16 } { 5 }$ 
D)  $\frac { 2 } { 5 }$

Question 8

Solve the problem.
-A car rental agency advertised renting a luxury, full-size car for $29.95 per day and $0.29 per mile. If you rent this car for 3 days, how many whole miles can you drive if you only have $200 to spend.

Accepted Answer

A) 66 mi 
B) 576 mi 
C) 379 mi 
D) 12 mi 
A) 66 mi 
B) 576 mi 
C) 379 mi 
D) 12 mi

Question 9

Solve the equation. Don't forget to first simplify each side of the equation, if possible.
-3(x + 6)= 4(x - 7)

Accepted Answer

A) -10 
B) 46 
C) all real numbers 
D) ø 
A) -10 
B) 46 
C) all real numbers 
D) ø

Question 10

Solve the equation.
-$- \frac { 3 } { 4 } \mathrm {~d} = \frac { 4 } { 9 }$

Accepted Answer

A)  $\frac { 32 } { 9 }$ 
B)  $- \frac { 27 } { 16 }$ 
C)  $- \frac { 16 } { 27 }$ 
D)  $\frac { 16 } { 27 }$ 
A)  $\frac { 32 } { 9 }$ 
B)  $- \frac { 27 } { 16 }$ 
C)  $- \frac { 16 } { 27 }$ 
D)  $\frac { 16 } { 27 }$

Question 11

Solve the equation. Don't forget to first simplify each side of the equation, if possible.
-$\frac { 2 } { 3 } x + \frac { 5 } { 6 } = - \frac { 1 } { 3 } x - \frac { 1 } { 2 }$

Accepted Answer

A)  $- \frac { 5 } { 8 }$ 
B)  $- \frac { 4 } { 3 }$ 
C)  $\frac { 4 } { 3 }$ 
D)  $\frac { 1 } { 3 }$ 
A)  $- \frac { 5 } { 8 }$ 
B)  $- \frac { 4 } { 3 }$ 
C)  $\frac { 4 } { 3 }$ 
D)  $\frac { 1 } { 3 }$

Question 12

Solve.
-The difference of triple a number andhe difference of triple a number and $\frac { 1 } { 2 }$ i s equal to the sum of the number and $\frac { 2 } { 3 }$ . Find the nu. Find the number.

Accepted Answer

A) - $- \frac { 7 } { 12 }$ 
B)  $\frac { 7 } { 12 }$ 
C)  $\frac { 13 } { 12 }$ 
D)  $\frac { 1 } { 12 }$ 
A) - $- \frac { 7 } { 12 }$ 
B)  $\frac { 7 } { 12 }$ 
C)  $\frac { 13 } { 12 }$ 
D)  $\frac { 1 } { 12 }$

Question 13

Write the algebraic expression described. Simplify if possible.
-In the race for Student Body President, Jose received 135 more votes than Angela. If Angela received x votes, how many votes did Jose receive?

Accepted Answer

A) (x - 135)votes 
B) (135 - x)votes 
C) (135x)votes 
D) (x + 135)votes 
A) (x - 135)votes 
B) (135 - x)votes 
C) (135x)votes 
D) (x + 135)votes

Question 14

Solve the equation.
-y - 12.8 = 7.2

Accepted Answer

A) 19.5 
B) 5.6 
C) 20 
D) 5.1 
A) 19.5 
B) 5.6 
C) 20 
D) 5.1

Question 15

Solve the equation.
--4x + 9 - 3x + 10 = 4

Accepted Answer

A) 15 
B)  $- \frac { 15 } { 7 }$ 
C)  $- \frac { 3 } { 7 }$ 
D)  $\frac { 15 } { 7 }$ 
A) 15 
B)  $- \frac { 15 } { 7 }$ 
C)  $- \frac { 3 } { 7 }$ 
D)  $\frac { 15 } { 7 }$

Question 16

Solve.
-A student scored 67, 84, and 94 on three algebra tests. What must he score on the fourth test in order to have an average grade of at least 85?

Accepted Answer

A) 95 
B) 29 
C) 61 
D) 82 
A) 95 
B) 29 
C) 61 
D) 82

Question 17

Solve the inequality.
-$\frac { x } { 5 } \geq 6$

Accepted Answer

A) $\{ x \mid x \leq 30 \}$ B) $\{ x \mid x > 30 \}$ C) $\{ x \mid x \geq 30 \}$ D) $\{ x \mid x < 30 \}$ A) $\{ x \mid x \leq 30 \}$ B) $\{ x \mid x > 30 \}$ C) $\{ x \mid x \geq 30 \}$ D) $\{ x \mid x < 30 \}$

Question 18

Solve the equation.
-$\frac { 1 } { 2 }$ (y(y + 2)= 5y

Accepted Answer

A)  $- \frac { 9 } { 2 }$ 
B)  $\frac { 9 } { 2 }$ 
C)  $- \frac { 2 } { 9 }$ 
D)  $\frac { 2 } { 9 }$ 
A)  $- \frac { 9 } { 2 }$ 
B)  $\frac { 9 } { 2 }$ 
C)  $- \frac { 2 } { 9 }$ 
D)  $\frac { 2 } { 9 }$

Question 19

Solve the equation.
-8x + 5(3x - 7)= -5 - 7x

Accepted Answer

A) 1 
B) - 1 
C)  $- \frac { 5 } { 2 }$ 
D)  $- \frac { 4 } { 3 }$ 
A) 1 
B) - 1 
C)  $- \frac { 5 } { 2 }$ 
D)  $- \frac { 4 } { 3 }$

Question 20

Solve the equation.
--45.6 = -7.6c

Accepted Answer

A) 2 
B) 38 
C) -38 
D) 6 
A) 2 
B) 38 
C) -38 
D) 6

Solve the equation. - $\frac { 2 x } { 5 } - \frac { x } { 3 }$ = 5

Solve. -When making a long distance call from a certain pay phone, the first three minutes of a call cost $2.75. After that, each additional minute or portion of a minute of that call costs $0.40. Use an inequality to find the Maximum number of minutes one can call long distance for $3.55.

Solve. -The manager of a coffee shop has one type of coffee that sells for $6 per pound and another type that sells for $12 per pound. The manager wishes to mix 100 pounds of the $12 coffee to get a mixture that will sell for $10 Per pound. How many pounds of the $6 coffee should be used?

Solve. Round to the nearest hundredth, if necessary. -20 is 9% of what number?

Solve the equation. -7(x + 4)+ 58 = 9x - 2(x - 7)

Solve. -The sum of four times a number and three is the same as the difference of twice the number and eleven. Find the number.

Solve the equation. - $\frac { 1 } { 5 }$ + x = 3

Solve the problem. -A car rental agency advertised renting a luxury, full-size car for $29.95 per day and $0.29 per mile. If you rent this car for 3 days, how many whole miles can you drive if you only have $200 to spend.

Solve the equation. Don't forget to first simplify each side of the equation, if possible. -3(x + 6)= 4(x - 7)

Solve the equation. - $- \frac { 3 } { 4 } \mathrm {~d} = \frac { 4 } { 9 }$

Solve the equation. Don't forget to first simplify each side of the equation, if possible. - $\frac { 2 } { 3 } x + \frac { 5 } { 6 } = - \frac { 1 } { 3 } x - \frac { 1 } { 2 }$

Solve. -The difference of triple a number andhe difference of triple a number and $\frac { 1 } { 2 }$ i s equal to the sum of the number and $\frac { 2 } { 3 }$ . Find the nu. Find the number.

Write the algebraic expression described. Simplify if possible. -In the race for Student Body President, Jose received 135 more votes than Angela. If Angela received x votes, how many votes did Jose receive?

Solve the equation. -y - 12.8 = 7.2

Solve the equation. --4x + 9 - 3x + 10 = 4

Solve. -A student scored 67, 84, and 94 on three algebra tests. What must he score on the fourth test in order to have an average grade of at least 85?

Solve the inequality. - $\frac { x } { 5 } \geq 6$ $Solve the inequality. - \frac { x } { 5 } \geq 6$

Solve the equation. - $\frac { 1 } { 2 }$ (y(y + 2)= 5y

Solve the equation. -8x + 5(3x - 7)= -5 - 7x

Solve the equation. --45.6 = -7.6c

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Exam 9: Equations, Inequalities, and Problem Solving

Solve the equation. - 2x5−x3\frac { 2 x } { 5 } - \frac { x } { 3 }52x​−3x​ = 5