Question 1

Solve: $$8 y - 5 \geq 7 y + 6$$

Accepted Answer

A) $y \geq 11$ B) $y > 11$ C) $y \leq 11$ D) $y < 11$ E) No solutions exist A) $y \geq 11$ B) $y > 11$ C) $y \leq 11$ D) $y < 11$ E) No solutions exist A

Question 2

Solve. $$25 + 4 x = 45 + 8 x$$

Accepted Answer

A)  x = 5 
B)  x = -12 
C)  x = 21 
D)  x = -21 
E)  x = -5 
A)  x = 5 
B)  x = -12 
C)  x = 21 
D)  x = -21 
E)  x = -5 E

Question 3

Solve the equation. $8 x + 5 = 4 ( 1 + x ) + 2$

Accepted Answer

A)  $x = \frac { 7 } { 8 }$ 
B)  $x = \frac { 1 } { 4 }$ 
C)  $x = - \frac { 7 } { 8 }$ 
D)  $x = - \frac { 1 } { 4 }$ 
E)  $x = \frac { 8 } { 7 }$ 
A)  $x = \frac { 7 } { 8 }$ 
B)  $x = \frac { 1 } { 4 }$ 
C)  $x = - \frac { 7 } { 8 }$ 
D)  $x = - \frac { 1 } { 4 }$ 
E)  $x = \frac { 8 } { 7 }$ B

Question 4

Solve the following inequality by using the Addition Property of Inequalities. $$x + 3 < 5$$

Accepted Answer

A) $x > 2$ B) $x > 3$ C) $x < 5$ D) $x < 2$ E) No solutions exist A) $x > 2$ B) $x > 3$ C) $x < 5$ D) $x < 2$ E) No solutions exist

Question 5

To solve 2(7 + 3x) = 3x + 8 from a graph, find the value of x where:

Accepted Answer

A)  y = 2(7 + 3x) intersects y = -4. 
B)  y = 2(7 + 3x) intersects the horizontal axis. 
C)  y = 3x + 8 intersects the horizontal axis. 
D)  y = 14 + 6x intersects y = 3x + 8. 
E)  y = 3x + 8 intersects y = -4. 
A)  y = 2(7 + 3x) intersects y = -4. 
B)  y = 2(7 + 3x) intersects the horizontal axis. 
C)  y = 3x + 8 intersects the horizontal axis. 
D)  y = 14 + 6x intersects y = 3x + 8. 
E)  y = 3x + 8 intersects y = -4.

Question 6

Solve. $8 x = 40$

Accepted Answer

A)  -8 
B)  5 
C)  -40 
D)  320 
E)  -5 
A)  -8 
B)  5 
C)  -40 
D)  320 
E)  -5

Question 7

Solve for x. $- 9 = 2 - 2 x$

Accepted Answer

A)  $x = 5 \frac { 1 } { 2 }$ 
B)  $x = 4 \frac { 1 } { 2 }$ 
C)  $x = 3 \frac { 1 } { 2 }$ 
D)  $x = 8 \frac { 1 } { 2 }$ 
E)  $x = 9 \frac { 1 } { 2 }$ 
A)  $x = 5 \frac { 1 } { 2 }$ 
B)  $x = 4 \frac { 1 } { 2 }$ 
C)  $x = 3 \frac { 1 } { 2 }$ 
D)  $x = 8 \frac { 1 } { 2 }$ 
E)  $x = 9 \frac { 1 } { 2 }$

Question 8

Use a calculator graph to solve the equation. $$9 x - 8 ( x + 2 ) = 8 ( x + 1 ) - 7 x$$

Accepted Answer

A)  x = 1 
B)  x = 3 
C)  x = 8 
D)  x = 4 
E)  { }, empty set, no real-number solution; the lines are parallel 
A)  x = 1 
B)  x = 3 
C)  x = 8 
D)  x = 4 
E)  { }, empty set, no real-number solution; the lines are parallel

Question 9

Solve. $$- 5 t - 4 = - 7 t - 20$$

Accepted Answer

A)  t = -11 
B)  t = 8 
C)  t = -8 
D)  t = 18 
E)  t = -3 
A)  t = -11 
B)  t = 8 
C)  t = -8 
D)  t = 18 
E)  t = -3

Question 10

Solve. $2 - 6 ( x + 3 ) = 2$

Accepted Answer

A)  x = 3 
B)  x = -3 
C)  x = -4 
D)  x = 24 
E)  x = 18 
A)  x = 3 
B)  x = -3 
C)  x = -4 
D)  x = 24 
E)  x = 18

Question 11

Solve. $$6 x + 28 = x - 17$$

Accepted Answer

A)  x = -9 
B)  x = -8 
C)  x = -11 
D)  x = -35 
E)  x = 52 
A)  x = -9 
B)  x = -8 
C)  x = -11 
D)  x = -35 
E)  x = 52

Question 12

Tell what was done to the first equation to get the second equation. $$x - 5 = - 2 , x = 3$$

Accepted Answer

A)  5 was subtracted from both sides of the first equation. 
B)  5 was added to both sides of the first equation. 
C)  Both sides of the first equation were multiplied by 5. 
D)  Both sides of the first equation were divided by 5. 
E)  -5 was added to both sides of the first equation. 
A)  5 was subtracted from both sides of the first equation. 
B)  5 was added to both sides of the first equation. 
C)  Both sides of the first equation were multiplied by 5. 
D)  Both sides of the first equation were divided by 5. 
E)  -5 was added to both sides of the first equation.

Question 13

Use two calculators tables to solve the equation. $$3 - 10 ( x - 8 ) = - 3 - 2 ( x - 13 )$$

Accepted Answer

A)  x = 5.5 
B)  x = 9.5 
C)  x = 6.5 
D)  x = 8.5 
E)  x = 7.5 
A)  x = 5.5 
B)  x = 9.5 
C)  x = 6.5 
D)  x = 8.5 
E)  x = 7.5

Question 14

State the inverse operation needed to solve the equation. Solve the equation. $- \frac { 3 } { 5 } x = 3$

Accepted Answer

A)  Multiply by $- \frac { 3 } { 5 } , x = - 5$ 
B)  Multiply by $- \frac { 5 } { 3 } , x = - 5$ 
C)  Multiply by $- \frac { 5 } { 3 } , x = 5$ 
D)  Multiply by $\frac { 5 } { 3 } , x = 5$ 
E)  Multiply by $\frac { 3 } { 5 } , x = - 5$ 
A)  Multiply by $- \frac { 3 } { 5 } , x = - 5$ 
B)  Multiply by $- \frac { 5 } { 3 } , x = - 5$ 
C)  Multiply by $- \frac { 5 } { 3 } , x = 5$ 
D)  Multiply by $\frac { 5 } { 3 } , x = 5$ 
E)  Multiply by $\frac { 3 } { 5 } , x = - 5$

Question 15

Write the sentence as an equation with x as the input, or independent, variable and y as the output, or dependent, variable. The output is five less than seven times the input.

Accepted Answer

A)  y = 7x + 5 
B)  y = 7x - 5 
C)  y = 5x - 7 
D)  y = 5 - 7x 
E)  y = 5 < 7x 
A)  y = 7x + 5 
B)  y = 7x - 5 
C)  y = 5x - 7 
D)  y = 5 - 7x 
E)  y = 5 < 7x

Question 16

Solve: $$3 x - 4 \geq 4 x + 6$$

Accepted Answer

A) $x \geq - 10$ B) $x > - 10$ C) $x \leq - 10$ D) $x < - 10$ E) No solutions exist A) $x \geq - 10$ B) $x > - 10$ C) $x \leq - 10$ D) $x < - 10$ E) No solutions exist

Question 17

Solve. $$18 x + 6 ( x - 5 ) = 118$$

Accepted Answer

A)  $6 \frac { 2 } { 7 }$ 
B)  $6 \frac { 1 } { 3 }$ 
C)  $7 \frac { 1 } { 6 }$ 
D)  $6 \frac { 1 } { 6 }$ 
E)  $7 \frac { 2 } { 7 }$ 
A)  $6 \frac { 2 } { 7 }$ 
B)  $6 \frac { 1 } { 3 }$ 
C)  $7 \frac { 1 } { 6 }$ 
D)  $6 \frac { 1 } { 6 }$ 
E)  $7 \frac { 2 } { 7 }$

Question 18

Solve. $3 z = - 15$

Accepted Answer

A)  -45 
B)  5 
C)  -5 
D)  -12 
E)  -18 
A)  -45 
B)  5 
C)  -5 
D)  -12 
E)  -18

Question 19

Write the equation. Let x be the unknown number. Eight is three more than two times a number.

Accepted Answer

A)  8 = 3x + 2 
B)  8 = 3x - 2 
C)  8 = 3 > 2x 
D)  8 = 2x - 3 
E)  8 = 2x + 3 
A)  8 = 3x + 2 
B)  8 = 3x - 2 
C)  8 = 3 > 2x 
D)  8 = 2x - 3 
E)  8 = 2x + 3

Question 20

Solve. $11 n - 5 = 6 n - 10$

Accepted Answer

A)  x = -5 
B)  x = -1 
C)  x = -10 
D)  x = 15 
E)  x = 5 
A)  x = -5 
B)  x = -1 
C)  x = -10 
D)  x = 15 
E)  x = 5

Solve: $8 y - 5 \geq 7 y + 6$

Solve. $25 + 4 x = 45 + 8 x$

Solve the equation. $8 x + 5 = 4 ( 1 + x ) + 2$

Solve the following inequality by using the Addition Property of Inequalities. $x + 3 < 5$

To solve 2(7 + 3x) = 3x + 8 from a graph, find the value of x where:

Solve. $8 x = 40$

Solve for x. $- 9 = 2 - 2 x$

Use a calculator graph to solve the equation. $9 x - 8 ( x + 2 ) = 8 ( x + 1 ) - 7 x$

Solve. $- 5 t - 4 = - 7 t - 20$

Solve. $2 - 6 ( x + 3 ) = 2$

Solve. $6 x + 28 = x - 17$

Tell what was done to the first equation to get the second equation. $x - 5 = - 2 , x = 3$

Use two calculators tables to solve the equation. $3 - 10 ( x - 8 ) = - 3 - 2 ( x - 13 )$

State the inverse operation needed to solve the equation. Solve the equation. $- \frac { 3 } { 5 } x = 3$

Write the sentence as an equation with x as the input, or independent, variable and y as the output, or dependent, variable. The output is five less than seven times the input.

Solve: $3 x - 4 \geq 4 x + 6$

Solve. $18 x + 6 ( x - 5 ) = 118$

Solve. $3 z = - 15$

Write the equation. Let x be the unknown number. Eight is three more than two times a number.

Solve. $11 n - 5 = 6 n - 10$

Algebraic Representations

Operations With Real Numbers

Ratios, Rates, and Proportional Reasoning

Formulas, Functions, Linear Equations, and Inequalities in Two Variables

Systems of Equations

Polynomial Expressions

Squares and Square Roots

Rational Expressions

Filters

Exam 3: Solving Equations

Solve: 8y−5≥7y+68 y - 5 \geq 7 y + 68y−5≥7y+6

Solve. 25+4x=45+8x25 + 4 x = 45 + 8 x25+4x=45+8x

Solve the equation. 8x+5=4(1+x)+28 x + 5 = 4 ( 1 + x ) + 28x+5=4(1+x)+2

Solve the following inequality by using the Addition Property of Inequalities. x+3<5x + 3 < 5x+3<5

To solve 2(7 + 3x) = 3x + 8 from a graph, find the value of x where:

Solve. 8x=408 x = 408x=40

Solve for x. −9=2−2x- 9 = 2 - 2 x−9=2−2x

Use a calculator graph to solve the equation. 9x−8(x+2)=8(x+1)−7x9 x - 8 ( x + 2 ) = 8 ( x + 1 ) - 7 x9x−8(x+2)=8(x+1)−7x

Solve. −5t−4=−7t−20- 5 t - 4 = - 7 t - 20−5t−4=−7t−20

Solve. 2−6(x+3)=22 - 6 ( x + 3 ) = 22−6(x+3)=2

Solve. 6x+28=x−176 x + 28 = x - 176x+28=x−17

Tell what was done to the first equation to get the second equation. x−5=−2,x=3x - 5 = - 2 , x = 3x−5=−2,x=3

Use two calculators tables to solve the equation. 3−10(x−8)=−3−2(x−13)3 - 10 ( x - 8 ) = - 3 - 2 ( x - 13 )3−10(x−8)=−3−2(x−13)

State the inverse operation needed to solve the equation. Solve the equation. −35x=3- \frac { 3 } { 5 } x = 3−53​x=3

Write the sentence as an equation with x as the input, or independent, variable and y as the output, or dependent, variable. The output is five less than seven times the input.

Solve: 3x−4≥4x+63 x - 4 \geq 4 x + 63x−4≥4x+6

Solve. 18x+6(x−5)=11818 x + 6 ( x - 5 ) = 11818x+6(x−5)=118

Solve. 3z=−153 z = - 153z=−15

Write the equation. Let x be the unknown number. Eight is three more than two times a number.

Solve. 11n−5=6n−1011 n - 5 = 6 n - 1011n−5=6n−10

Algebraic Representations

Operations With Real Numbers

Ratios, Rates, and Proportional Reasoning

Formulas, Functions, Linear Equations, and Inequalities in Two Variables

Systems of Equations

Polynomial Expressions

Squares and Square Roots

Rational Expressions

Filters

Solve: $8 y - 5 \geq 7 y + 6$

Solve. $25 + 4 x = 45 + 8 x$

Solve the equation. $8 x + 5 = 4 ( 1 + x ) + 2$

Solve the following inequality by using the Addition Property of Inequalities. $x + 3 < 5$

Solve. $8 x = 40$

Solve for x. $- 9 = 2 - 2 x$

Use a calculator graph to solve the equation. $9 x - 8 ( x + 2 ) = 8 ( x + 1 ) - 7 x$

Solve. $- 5 t - 4 = - 7 t - 20$

Solve. $2 - 6 ( x + 3 ) = 2$

Solve. $6 x + 28 = x - 17$

Tell what was done to the first equation to get the second equation. $x - 5 = - 2 , x = 3$

Use two calculators tables to solve the equation. $3 - 10 ( x - 8 ) = - 3 - 2 ( x - 13 )$

State the inverse operation needed to solve the equation. Solve the equation. $- \frac { 3 } { 5 } x = 3$

Solve: $3 x - 4 \geq 4 x + 6$

Solve. $18 x + 6 ( x - 5 ) = 118$

Solve. $3 z = - 15$

Solve. $11 n - 5 = 6 n - 10$