Question 1

Solve the inequality. $$4 x + 9 \geq 3 x + 14$$

Accepted Answer

A) $x > 5$ B) $x \neq 5$ C) $x \geq 5$ D) $x < 5$ E) $x \leq 5$ A) $x > 5$ B) $x \neq 5$ C) $x \geq 5$ D) $x < 5$ E) $x \leq 5$ C

Question 2

When two lines intersect as in the illustration below, four angles are formed. Angles that are side-by-side, such as $\angle 1$ and $\angle 2$ , are called adjacent angles. Angles that are nonadjacent, such as $\angle 1$ and $\angle 3$ or $\angle 2$ and $\angle 4$ , are called vertical angles. From geometry, we know that if two lines intersect, vertical angles have the same measure. If $m ( \angle 1 ) = ( 5 x + 10 ) ^ { \circ }$ and $m ( \angle 3 ) = ( 7 x - 10 ) ^ { \circ }$ , find x . Read $m ( \angle 1 )$ as "the measure of $\angle 1$ ".

Accepted Answer

A) x = 11 
B) x = 15 
C) x = 6 
D) x = 8 
E) x = 10 
A) x = 11 
B) x = 15 
C) x = 6 
D) x = 8 
E) x = 10 E

Question 3

Solve the formula $i = p r t$ for the variable r . Then substitute numbers i = 90 , p = 200, and t = 5 to find the variable's value.

Accepted Answer

A) r = 105 
B) r = - 115 
C) r = 0.09 
D) r = 295 
E) r = 0.45 
A) r = 105 
B) r = - 115 
C) r = 0.09 
D) r = 295 
E) r = 0.45 C

Question 4

Graph the solution set. $$0.4 > 3 x - 0.02$$

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

Eva invested a certain amount of money at 13% interest and $2,500 more than that amount at 15%. Her total yearly interest was $1,775. How much did she invest at each rate?

Accepted Answer

A) $2,500 at 13%, $5,000 at 15% 
B) $5,000 at 13%, $7,500 at 15% 
C) $5,200 at 13%, $7,300 at 15% 
D) $5,200 at 13%, $7,700 at 15% 
E) $7,500 at 13%, $5,000 at 15% 
A) $2,500 at 13%, $5,000 at 15% 
B) $5,000 at 13%, $7,500 at 15% 
C) $5,200 at 13%, $7,300 at 15% 
D) $5,200 at 13%, $7,700 at 15% 
E) $7,500 at 13%, $5,000 at 15%

Question 6

Solve the inequality. $4 ( x + 5 ) > 12$

Accepted Answer

A)  $x  - 2$ 
A)  $x  - 2$

Question 7

The perimeter $P$ of a rectangle with length I and width W is given by the formula $P = 2 l + 2 w$ . Solve this formula for W . If the perimeter of a certain rectangle is 46.54 meters and its length is 16.25 meters, find its width.

Accepted Answer

A)  $w = \frac { P - 2 l } { 2 } ; w = 4.83 \mathrm {~m}$ 
B)  $w = \frac { 2 l - P } { 2 } ; w = 7.02 \mathrm {~m}$ 
C)  $w = P - 2 l ; \quad w = 14.04 \mathrm {~m}$ 
D)  $w = \frac { P - 2 l } { 2 } ; w = 7.02 \mathrm {~m}$ 
E)  $w = 2 l - P ; \quad w = 4.83 \mathrm {~m}$ 
A)  $w = \frac { P - 2 l } { 2 } ; w = 4.83 \mathrm {~m}$ 
B)  $w = \frac { 2 l - P } { 2 } ; w = 7.02 \mathrm {~m}$ 
C)  $w = P - 2 l ; \quad w = 14.04 \mathrm {~m}$ 
D)  $w = \frac { P - 2 l } { 2 } ; w = 7.02 \mathrm {~m}$ 
E)  $w = 2 l - P ; \quad w = 4.83 \mathrm {~m}$

Question 8

Solve the equation, if possible. $$| 5 x + 7 | = - | 9 x - 2 |$$

Accepted Answer

A)  $1 , - 9$ 
B)  $1,9$ 
C)  $- 9 , - 1$ 
D)  $- 5 , - 1$ 
E) no solution 
A)  $1 , - 9$ 
B)  $1,9$ 
C)  $- 9 , - 1$ 
D)  $- 5 , - 1$ 
E) no solution

Question 9

Solve the inequality and express the solution set using interval notation. $8 ( 7 - x ) \leq 10 ( 7 - x )$

Accepted Answer

A)  $[ 8 , \infty )$ 
B)  $( - \infty , 8 ]$ 
C)  $[ 7 , \infty )$ 
D)  $( - \infty , 7 ]$ 
E)  $[ 7 , \infty ]$ 
A)  $[ 8 , \infty )$ 
B)  $( - \infty , 8 ]$ 
C)  $[ 7 , \infty )$ 
D)  $( - \infty , 7 ]$ 
E)  $[ 7 , \infty ]$

Question 10

Solve the equation. 0.11 t - 2.1 = 0.06 t - 0.3

Accepted Answer

A) t = -36 
B) t = 108 
C) t = 36 
D) t = 72 
E) t = 34 
A) t = -36 
B) t = 108 
C) t = 36 
D) t = 72 
E) t = 34

Question 11

Solve the formula $V = I T$ for the variable $T$ .

Accepted Answer

A)  $T = \frac { I } { V }$ 
B)  $T = V I$ 
C)  $T = \frac { V } { I }$ 
D)  $\frac { 1 } { T } = \frac { V } { I }$ 
E)  $T = \frac { 1 } { V I }$ 
A)  $T = \frac { I } { V }$ 
B)  $T = V I$ 
C)  $T = \frac { V } { I }$ 
D)  $\frac { 1 } { T } = \frac { V } { I }$ 
E)  $T = \frac { 1 } { V I }$

Question 12

Use an algebraic approach to solve the problem: Suppose that the width of a certain rectangle is 2 inch more than one-fourth of its length. The perimeter of the rectangle is 24 inches. Find the length and width of the rectangle.

Accepted Answer

A) 5 inches wide, 7 inches long 
B) 2 inches wide, 10 inches long 
C) 3 inches wide, 9 inches long 
D) 4 inches wide, 8 inches long 
E) 7 inches wide, 5 inches long 
A) 5 inches wide, 7 inches long 
B) 2 inches wide, 10 inches long 
C) 3 inches wide, 9 inches long 
D) 4 inches wide, 8 inches long 
E) 7 inches wide, 5 inches long

Question 13

Solve the inequality. Write the answer in interval notation. $6 - x < 4 < 7 - x$

Accepted Answer

A)  $( - 3 , - 2 )$ 
B)  $( - \infty , \infty )$ 
C)  $( 2,3 )$ 
D) no solution 
A)  $( - 3 , - 2 )$ 
B)  $( - \infty , \infty )$ 
C)  $( 2,3 )$ 
D) no solution

Question 14

For the following problem, solve the inequality and express the solution set using interval notation. $8 x - 48 - 2 x > 36$

Accepted Answer

A)  $( 15 , \infty )$ 
B)  $( 14 , \infty )$ 
C)  $( 13 , \infty )$ 
D)  $( - 14 , \infty )$ 
E) none of these 
A)  $( 15 , \infty )$ 
B)  $( 14 , \infty )$ 
C)  $( 13 , \infty )$ 
D)  $( - 14 , \infty )$ 
E) none of these

Question 15

Use the properties of equality to solve the equation. $$\frac { 11 } { 12 } a = \frac { 1 } { 3 }$$

Accepted Answer

A)  $a = \frac { 1 } { 12 }$ 
B)  $a = \frac { 4 } { 11 }$ 
C)  $a = \frac { 1 } { 11 }$ 
D)  $a = \frac { 4 } { 3 }$ 
E) none of these 
A)  $a = \frac { 1 } { 12 }$ 
B)  $a = \frac { 4 } { 11 }$ 
C)  $a = \frac { 1 } { 11 }$ 
D)  $a = \frac { 4 } { 3 }$ 
E) none of these

Question 16

Solve the inequality. -2 x ≥ 6

Accepted Answer

A) x ≥ -3 
B) x ≠ -3 
C) x ≤ 3 
D) x 
E) x ≤ -3 
A) x ≥ -3 
B) x ≠ -3 
C) x ≤ 3 
D) x 
E) x ≤ -3

Question 17

Solve the equation. n + 0.5 n = 90

Accepted Answer

A) n = 90 
B) n = 0.5 
C) n = -29.5 
D) n = 60 
E) n = 149.5 
A) n = 90 
B) n = 0.5 
C) n = -29.5 
D) n = 60 
E) n = 149.5

Question 18

Use an equation to solve the problem. The average price of homes in one neighborhood decreased 8% since last year, a drop of $5,400. What was the average price of a home last year?

Accepted Answer

A) $64,500 
B) $69,500 
C) $68,500 
D) $67,500 
E) $71,500 
A) $64,500 
B) $69,500 
C) $68,500 
D) $67,500 
E) $71,500

Question 19

Use an equation to solve the problem. Sales tax on a $14 compact disc is $0.84. At what rate is sales tax computed?

Accepted Answer

A) 2% 
B) 6% 
C) 8% 
D) 5% 
E) 3% 
A) 2% 
B) 6% 
C) 8% 
D) 5% 
E) 3%

Question 20

Use an algebraic approach to solve the problem: Find a number such that one-half of the number is 5 less than two-thirds of the number.

Accepted Answer

A) 15 
B) 30 
C) 25 
D) 35 
E) 20 
A) 15 
B) 30 
C) 25 
D) 35 
E) 20

Solve the inequality. $4 x + 9 \geq 3 x + 14$

Solve the formula $i = p r t$ for the variable r . Then substitute numbers i = 90 , p = 200, and t = 5 to find the variable's value.

Graph the solution set. $0.4 > 3 x - 0.02$

Eva invested a certain amount of money at 13% interest and $2,500 more than that amount at 15%. Her total yearly interest was $1,775. How much did she invest at each rate?

Solve the inequality. $4 ( x + 5 ) > 12$

The perimeter $P$ of a rectangle with length I and width W is given by the formula $P = 2 l + 2 w$ . Solve this formula for W . If the perimeter of a certain rectangle is 46.54 meters and its length is 16.25 meters, find its width.

Solve the equation, if possible. $| 5 x + 7 | = - | 9 x - 2 |$

Solve the inequality and express the solution set using interval notation. $8 ( 7 - x ) \leq 10 ( 7 - x )$

Solve the equation. 0.11 t - 2.1 = 0.06 t - 0.3

Solve the formula $V = I T$ for the variable $T$ .

Use an algebraic approach to solve the problem: Suppose that the width of a certain rectangle is 2 inch more than one-fourth of its length. The perimeter of the rectangle is 24 inches. Find the length and width of the rectangle.

Solve the inequality. Write the answer in interval notation. $6 - x < 4 < 7 - x$

For the following problem, solve the inequality and express the solution set using interval notation. $8 x - 48 - 2 x > 36$

Use the properties of equality to solve the equation. $\frac { 11 } { 12 } a = \frac { 1 } { 3 }$

Solve the inequality. -2 x ≥ 6

Solve the equation. n + 0.5 n = 90

Use an equation to solve the problem. The average price of homes in one neighborhood decreased 8% since last year, a drop of $5,400. What was the average price of a home last year?

Use an equation to solve the problem. Sales tax on a $14 compact disc is $0.84. At what rate is sales tax computed?

Use an algebraic approach to solve the problem: Find a number such that one-half of the number is 5 less than two-thirds of the number.

Basic Concepts and Properties

Polynomials

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

Filters

Exam 2: Equations, Inequalities, and Problem Solving

Solve the inequality. 4x+9≥3x+144 x + 9 \geq 3 x + 144x+9≥3x+14

Solve the formula i=prti = p r ti=prt for the variable r . Then substitute numbers i = 90 , p = 200, and t = 5 to find the variable's value.

Graph the solution set. 0.4>3x−0.020.4 > 3 x - 0.020.4>3x−0.02

Eva invested a certain amount of money at 13% interest and $2,500 more than that amount at 15%. Her total yearly interest was $1,775. How much did she invest at each rate?

Solve the inequality. 4(x+5)>124 ( x + 5 ) > 124(x+5)>12

The perimeter PPP of a rectangle with length I and width W is given by the formula P=2l+2wP = 2 l + 2 wP=2l+2w . Solve this formula for W . If the perimeter of a certain rectangle is 46.54 meters and its length is 16.25 meters, find its width.

Solve the equation, if possible. ∣5x+7∣=−∣9x−2∣| 5 x + 7 | = - | 9 x - 2 |∣5x+7∣=−∣9x−2∣

Solve the inequality and express the solution set using interval notation. 8(7−x)≤10(7−x)8 ( 7 - x ) \leq 10 ( 7 - x )8(7−x)≤10(7−x)

Solve the equation. 0.11 t - 2.1 = 0.06 t - 0.3

Solve the formula V=ITV = I TV=IT for the variable TTT .

Use an algebraic approach to solve the problem: Suppose that the width of a certain rectangle is 2 inch more than one-fourth of its length. The perimeter of the rectangle is 24 inches. Find the length and width of the rectangle.

Solve the inequality. Write the answer in interval notation. 6−x<4<7−x6 - x < 4 < 7 - x6−x<4<7−x

For the following problem, solve the inequality and express the solution set using interval notation. 8x−48−2x>368 x - 48 - 2 x > 368x−48−2x>36

Use the properties of equality to solve the equation. 1112a=13\frac { 11 } { 12 } a = \frac { 1 } { 3 }1211​a=31​

Solve the inequality. -2 x ≥ 6

Solve the equation. n + 0.5 n = 90

Use an equation to solve the problem. The average price of homes in one neighborhood decreased 8% since last year, a drop of $5,400. What was the average price of a home last year?

Use an equation to solve the problem. Sales tax on a $14 compact disc is $0.84. At what rate is sales tax computed?

Use an algebraic approach to solve the problem: Find a number such that one-half of the number is 5 less than two-thirds of the number.

Basic Concepts and Properties

Polynomials

Rational Expressions

Exponents and Radicals

Quadratic Equations and Inequalities

Equations and Inequalities in Two Variables

Conic Sections

Functions

Systems of Equations

Exponential and Logarithmic Functions

Filters

Solve the inequality. $4 x + 9 \geq 3 x + 14$

Solve the formula $i = p r t$ for the variable r . Then substitute numbers i = 90 , p = 200, and t = 5 to find the variable's value.

Graph the solution set. $0.4 > 3 x - 0.02$

Solve the inequality. $4 ( x + 5 ) > 12$

The perimeter $P$ of a rectangle with length I and width W is given by the formula $P = 2 l + 2 w$ . Solve this formula for W . If the perimeter of a certain rectangle is 46.54 meters and its length is 16.25 meters, find its width.

Solve the equation, if possible. $| 5 x + 7 | = - | 9 x - 2 |$

Solve the inequality and express the solution set using interval notation. $8 ( 7 - x ) \leq 10 ( 7 - x )$

Solve the formula $V = I T$ for the variable $T$ .

Solve the inequality. Write the answer in interval notation. $6 - x < 4 < 7 - x$

For the following problem, solve the inequality and express the solution set using interval notation. $8 x - 48 - 2 x > 36$

Use the properties of equality to solve the equation. $\frac { 11 } { 12 } a = \frac { 1 } { 3 }$