Question 1

Solve the equation. $$\frac { 3 } { 10 } ( 3 - 2 x ) = 3$$

Accepted Answer

A)  $x = - 3.5$ 
B)  $x = - 2.5$ 
C)  $x = 2.5$ 
D)  $x = 3.5$ 
E)  $x = 4.5$ 
A)  $x = - 3.5$ 
B)  $x = - 2.5$ 
C)  $x = 2.5$ 
D)  $x = 3.5$ 
E)  $x = 4.5$

Question 2

Solve the equation from the table. $$11 - x = 10$$ $x \quad y = 11 - x$
1
10
2
9
3
8
4
7

Accepted Answer

A)  $x = 1$ 
B)  $x = 12$ 
C)  $x = 4$ 
D)  $x = 3$ 
E)  $x = 21$ 
A)  $x = 1$ 
B)  $x = 12$ 
C)  $x = 4$ 
D)  $x = 3$ 
E)  $x = 21$

Question 3

Solve. $- 7 t = 56$

Accepted Answer

A)  -392 
B)  8 
C)  49 
D)  -8 
E)  63 
A)  -392 
B)  8 
C)  49 
D)  -8 
E)  63

Question 4

Write the following problem as an equation and solve. The sum of a number and 1 is 6.

Accepted Answer

A)  $x + 1 = 6$ ; -5 
B)  $x + 6 = 1$ ; 5 
C)  $x + 6 = 1$ ; -5 
D)  $x + 1 = 6$ ; 5 
E)  $x + 1 = 6$ ; 3 
A)  $x + 1 = 6$ ; -5 
B)  $x + 6 = 1$ ; 5 
C)  $x + 6 = 1$ ; -5 
D)  $x + 1 = 6$ ; 5 
E)  $x + 1 = 6$ ; 3

Question 5

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 more than negative two times the input.

Accepted Answer

A)  y = 2x + 5 
B)  y = 5x + 2 
C)  y = 5x - 2 
D)  y = -2x - 5 
E)  y = -2x + 5 
A)  y = 2x + 5 
B)  y = 5x + 2 
C)  y = 5x - 2 
D)  y = -2x - 5 
E)  y = -2x + 5

Question 6

Write the equation for the sentence. Let x be the unknown number. Three times a number is 2.3.

Accepted Answer

A)  3 + x = 2.3 
B)  3 - x = 2.3 
C)  3x = 2.3 
D)  x - 3 = 2.3 
E)  $\frac { x } { 3 } = 2.3$ 
A)  3 + x = 2.3 
B)  3 - x = 2.3 
C)  3x = 2.3 
D)  x - 3 = 2.3 
E)  $\frac { x } { 3 } = 2.3$

Question 7

Write the following problem as an equation and solve. A number decreased by 3 is 2.

Accepted Answer

A)  $x - 3 = 2$ ; 1 
B)  $x + 2 = 3$ ; 5 
C)  $x - 3 = 2$ ; 5 
D)  $x - 2 = 3$ ; 1 
E)  $x - 3 = 2$ ; -1 
A)  $x - 3 = 2$ ; 1 
B)  $x + 2 = 3$ ; 5 
C)  $x - 3 = 2$ ; 5 
D)  $x - 2 = 3$ ; 1 
E)  $x - 3 = 2$ ; -1

Question 8

Use a calculator graph to solve the equation. $$2 ( x + 2 ) = 3 x - 1$$

Accepted Answer

A)  x = 7 
B)  x = 5 
C)  x = 4 
D)  x = 3 
E)  { }, empty set, no real-number solution; the lines are parallel 
A)  x = 7 
B)  x = 5 
C)  x = 4 
D)  x = 3 
E)  { }, empty set, no real-number solution; the lines are parallel

Question 9

Solve the following inequality by using the Addition Property of Inequalities. $$n - 2 < - 10$$

Accepted Answer

A) $n > - 8$ B) $n > 2$ C) $n < - 10$ D) $n < - 8$ E) No solutions exist A) $n > - 8$ B) $n > 2$ C) $n < - 10$ D) $n < - 8$ E) No solutions exist

Question 10

Write the sentence as a two variable equation containing parentheses. Describe your variables so y depends on x. A DVD rental is $7 for two days and a penalty of $8 for each additional day.

Accepted Answer

A)  y = 7 for $x \leq 2$ days; y = 7 +8(x - 2) for x > 2 
B)  y = 7 for $x \leq 2$ days; y = 7 +8(x - 1) for x > 1 
C)  y = 7 for $x \leq 2$ days; y = 7 +(8 - 1)x for x > 2. 
D)  y = 7 for $x \leq 2$ days; y = 8 +7(x - 2) for x > 2. 
E)  y = 7 for $x \leq 2$ days; y = 7 +8(x - 1) for x > 1. 
A)  y = 7 for $x \leq 2$ days; y = 7 +8(x - 2) for x > 2 
B)  y = 7 for $x \leq 2$ days; y = 7 +8(x - 1) for x > 1 
C)  y = 7 for $x \leq 2$ days; y = 7 +(8 - 1)x for x > 2. 
D)  y = 7 for $x \leq 2$ days; y = 8 +7(x - 2) for x > 2. 
E)  y = 7 for $x \leq 2$ days; y = 7 +8(x - 1) for x > 1.

Question 11

Solve the equation to find the cash advance for a 3% credit card fee. 0.03x = 10.80

Accepted Answer

A)  x = 32.4 
B)  x = 324 
C)  x = 36 
D)  x = 3.6 
E)  x = 360 
A)  x = 32.4 
B)  x = 324 
C)  x = 36 
D)  x = 3.6 
E)  x = 360

Question 12

State the inverse operation needed to solve the equation. Solve the equation. $$x - \frac { 7 } { 9 } = 15$$

Accepted Answer

A)  Add $\frac { 7 } { 9 }$ ; x = $15 \frac { 7 } { 9 }$ 
B)  Subtract $\frac { 7 } { 9 }$ ; x = $15 \frac { 7 } { 9 }$ 
C)  Add $\frac { 7 } { 9 }$ ; x = $14 \frac { 7 } { 9 }$ 
D)  Subtract $\frac { 7 } { 9 }$ ; x = $14 \frac { 7 } { 9 }$ 
E)  Add $\frac { 7 } { 9 }$ ; x = $13 \frac { 7 } { 9 }$ 
A)  Add $\frac { 7 } { 9 }$ ; x = $15 \frac { 7 } { 9 }$ 
B)  Subtract $\frac { 7 } { 9 }$ ; x = $15 \frac { 7 } { 9 }$ 
C)  Add $\frac { 7 } { 9 }$ ; x = $14 \frac { 7 } { 9 }$ 
D)  Subtract $\frac { 7 } { 9 }$ ; x = $14 \frac { 7 } { 9 }$ 
E)  Add $\frac { 7 } { 9 }$ ; x = $13 \frac { 7 } { 9 }$

Question 13

Write the sentence as an equation containing parentheses. Solve the equation. At an outdoor concert, the staff adds 4 seats to each row of x seats. There are 25 rows altogether, and there are 1,200 seats altogether. How many seats, x, were in the original rows?

Accepted Answer

A)  $1,200 = 25 ( x + 4 ) ; x = 44 \text { seats }$ 
B)  $1,200 = 25 ( x + 4 ) ; \quad x = 43 \text { seats }$ 
C)  $1200 = 25 ( x + 3 ) ; x = 44 \text { seats }$ 
D)  $1200 = 25 ( x - 3 ) ; x = 44 \text { seats }$ 
E)  $1200 = 25 ( x - 3 ) ; x = 43 \text { seats }$ 
A)  $1,200 = 25 ( x + 4 ) ; x = 44 \text { seats }$ 
B)  $1,200 = 25 ( x + 4 ) ; \quad x = 43 \text { seats }$ 
C)  $1200 = 25 ( x + 3 ) ; x = 44 \text { seats }$ 
D)  $1200 = 25 ( x - 3 ) ; x = 44 \text { seats }$ 
E)  $1200 = 25 ( x - 3 ) ; x = 43 \text { seats }$

Question 14

Write the equation as a sentence: x + 4 = -10.

Accepted Answer

A)  The difference between a number and 4 is -10. 
B)  The product of a number and 4 is -10. 
C)  The quotient of a number and 4 is -10. 
D)  The difference between 4 and a number is -10. 
E)  The sum of a number and 4 is -10. 
A)  The difference between a number and 4 is -10. 
B)  The product of a number and 4 is -10. 
C)  The quotient of a number and 4 is -10. 
D)  The difference between 4 and a number is -10. 
E)  The sum of a number and 4 is -10.

Question 15

Solve the equation. $$2 - 3 ( 3 - x ) = 5$$

Accepted Answer

A)  $x = 3$ 
B)  $x = 4$ 
C)  $x = - 3$ 
D)  $x = 6$ 
E)  $x = - 4$ 
A)  $x = 3$ 
B)  $x = 4$ 
C)  $x = - 3$ 
D)  $x = 6$ 
E)  $x = - 4$

Question 16

Solve the following inequality by using the Addition Property of Inequalities. $$m - 2 \leq - 6$$

Accepted Answer

A) $m \geq - 4$ B) $m > - 4$ C) $m \leq - 4$ D) $m < - 4$ E) No solutions exist A) $m \geq - 4$ B) $m > - 4$ C) $m \leq - 4$ D) $m < - 4$ E) No solutions exist

Question 17

Tell what was done to the first equation to get the second equation. $$5 x = 35 ; x = 7$$

Accepted Answer

A)  Both sides of the first equation were divided by 5. 
B)  Both sides of the first equation were multiplied by 5. 
C)  28 was added to both sides of the first equation. 
D)  28 was subtracted from both sides of the first equation. 
E)  Both sides of the first equation were divided by 7. 
A)  Both sides of the first equation were divided by 5. 
B)  Both sides of the first equation were multiplied by 5. 
C)  28 was added to both sides of the first equation. 
D)  28 was subtracted from both sides of the first equation. 
E)  Both sides of the first equation were divided by 7.

Question 18

Solve. $$5 x + 25 = 2 x + 4$$

Accepted Answer

A)  x = 29 
B)  x = -13 
C)  x = -21 
D)  x = -28 
E)  x = -7 
A)  x = 29 
B)  x = -13 
C)  x = -21 
D)  x = -28 
E)  x = -7

Question 19

Solve: $$b - 4 \geq - 5$$

Accepted Answer

A) $b \geq - 1$ B) $b > - 1$ C) $b \leq - 1$ D) $b < - 1$ E) No solutions exist A) $b \geq - 1$ B) $b > - 1$ C) $b \leq - 1$ D) $b < - 1$ E) No solutions exist

Question 20

The Valley Inn charges $37.50 per person and a $500 service charge. Write and solve an inequality that shows the number of persons (x) who can attend a wedding reception on a $3650 budget.

Accepted Answer

A)  x $\leq$ 84 
B)  x $\leq$ 97 
C)  x $\leq$ 110 
D)  x $\geq$ 97 
E)  x $\leq$ 75 
A)  x $\leq$ 84 
B)  x $\leq$ 97 
C)  x $\leq$ 110 
D)  x $\geq$ 97 
E)  x $\leq$ 75

Solve the equation. $\frac { 3 } { 10 } ( 3 - 2 x ) = 3$

Solve the equation from the table. $11 - x = 10$ $x \quad y = 11 - x$ 1 10 2 9 3 8 4 7

Solve. $- 7 t = 56$

Write the following problem as an equation and solve. The sum of a number and 1 is 6.

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 more than negative two times the input.

Write the equation for the sentence. Let x be the unknown number. Three times a number is 2.3.

Write the following problem as an equation and solve. A number decreased by 3 is 2.

Use a calculator graph to solve the equation. $2 ( x + 2 ) = 3 x - 1$

Solve the following inequality by using the Addition Property of Inequalities. $n - 2 < - 10$

Write the sentence as a two variable equation containing parentheses. Describe your variables so y depends on x. A DVD rental is $7 for two days and a penalty of $8 for each additional day.

Solve the equation to find the cash advance for a 3% credit card fee. 0.03x = 10.80

State the inverse operation needed to solve the equation. Solve the equation. $x - \frac { 7 } { 9 } = 15$

Write the sentence as an equation containing parentheses. Solve the equation. At an outdoor concert, the staff adds 4 seats to each row of x seats. There are 25 rows altogether, and there are 1,200 seats altogether. How many seats, x, were in the original rows?

Write the equation as a sentence: x + 4 = -10.

Solve the equation. $2 - 3 ( 3 - x ) = 5$

Solve the following inequality by using the Addition Property of Inequalities. $m - 2 \leq - 6$

Tell what was done to the first equation to get the second equation. $5 x = 35 ; x = 7$

Solve. $5 x + 25 = 2 x + 4$

Solve: $b - 4 \geq - 5$

The Valley Inn charges $37.50 per person and a $500 service charge. Write and solve an inequality that shows the number of persons (x) who can attend a wedding reception on a $3650 budget.

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 the equation. 310(3−2x)=3\frac { 3 } { 10 } ( 3 - 2 x ) = 3103​(3−2x)=3

Solve the equation from the table. 11−x=1011 - x = 1011−x=10 xy=11−xx \quad y = 11 - xxy=11−x 1 10 2 9 3 8 4 7

Solve. −7t=56- 7 t = 56−7t=56

Write the following problem as an equation and solve. The sum of a number and 1 is 6.

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 more than negative two times the input.

Write the equation for the sentence. Let x be the unknown number. Three times a number is 2.3.

Write the following problem as an equation and solve. A number decreased by 3 is 2.

Use a calculator graph to solve the equation. 2(x+2)=3x−12 ( x + 2 ) = 3 x - 12(x+2)=3x−1

Solve the following inequality by using the Addition Property of Inequalities. n−2<−10n - 2 < - 10n−2<−10

Write the sentence as a two variable equation containing parentheses. Describe your variables so y depends on x. A DVD rental is $7 for two days and a penalty of $8 for each additional day.

Solve the equation to find the cash advance for a 3% credit card fee. 0.03x = 10.80

State the inverse operation needed to solve the equation. Solve the equation. x−79=15x - \frac { 7 } { 9 } = 15x−97​=15

Write the sentence as an equation containing parentheses. Solve the equation. At an outdoor concert, the staff adds 4 seats to each row of x seats. There are 25 rows altogether, and there are 1,200 seats altogether. How many seats, x, were in the original rows?

Write the equation as a sentence: x + 4 = -10.

Solve the equation. 2−3(3−x)=52 - 3 ( 3 - x ) = 52−3(3−x)=5

Solve the following inequality by using the Addition Property of Inequalities. m−2≤−6m - 2 \leq - 6m−2≤−6

Tell what was done to the first equation to get the second equation. 5x=35;x=75 x = 35 ; x = 75x=35;x=7

Solve. 5x+25=2x+45 x + 25 = 2 x + 45x+25=2x+4

Solve: b−4≥−5b - 4 \geq - 5b−4≥−5

The Valley Inn charges $37.50 per person and a $500 service charge. Write and solve an inequality that shows the number of persons (x) who can attend a wedding reception on a $3650 budget.

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 the equation. $\frac { 3 } { 10 } ( 3 - 2 x ) = 3$

Solve the equation from the table. $11 - x = 10$ $x \quad y = 11 - x$ 1 10 2 9 3 8 4 7

Solve. $- 7 t = 56$

Use a calculator graph to solve the equation. $2 ( x + 2 ) = 3 x - 1$

Solve the following inequality by using the Addition Property of Inequalities. $n - 2 < - 10$

State the inverse operation needed to solve the equation. Solve the equation. $x - \frac { 7 } { 9 } = 15$

Solve the equation. $2 - 3 ( 3 - x ) = 5$

Solve the following inequality by using the Addition Property of Inequalities. $m - 2 \leq - 6$

Tell what was done to the first equation to get the second equation. $5 x = 35 ; x = 7$

Solve. $5 x + 25 = 2 x + 4$

Solve: $b - 4 \geq - 5$