Question 1

Solve the inequality. Other than Ø, graph the solution set on a number line.
-$$- 6 x + 8 - 4 x < 8 - 12 x + 6$$

Accepted Answer

A)  $( 3 , \infty )$
  
B)  $( \infty , 3 )$
  
C)  $( \infty , 3 ]$
  
D)  $[ 3 , \infty )$
  
A)  $( 3 , \infty )$
  
B)  $( \infty , 3 )$
  
C)  $( \infty , 3 ]$
  
D)  $[ 3 , \infty )$

Question 2

Solve and graph the solution set on a number line.
-$$| 3 ( x + 1 ) + 9 | \geq 15$$

Accepted Answer

A)  $[ - 9,1 ]$
  
B)  $( \infty , - 7 ] \cup [ 3 , \infty )$
  
C)  $[ - 7,3 ]$
  
D)  $( * , - 9 ] \cup [ 1 , \infty )$
  
A)  $[ - 9,1 ]$
  
B)  $( \infty , - 7 ] \cup [ 3 , \infty )$
  
C)  $[ - 7,3 ]$
  
D)  $( * , - 9 ] \cup [ 1 , \infty )$

Question 3

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
-$4 x  5$

Accepted Answer

A)  $[ 1,3 ]$
  
B)  $( 1,3 )$
  
C)  $( - \infty , 1 ) \cup ( 3 , \infty )$
  
D) 
$\varnothing$ 
A)  $[ 1,3 ]$
  
B)  $( 1,3 )$
  
C)  $( - \infty , 1 ) \cup ( 3 , \infty )$
  
D) 
$\varnothing$

Question 4

Solve.
-The length ℓ of a metal rod used in manufacturing cars must not differ from the standard s by more than 0.3 inches. The manufacturing engineers express this as |ℓ- s| ≤0.3. If the standard s is 23.1, solve the inequality for the length ℓ. Express the answer in set-builder notation.

Accepted Answer

A)  $\{ \ell l \ell \leq 22.8$ or $\ell \geq 23.4 \}$ 
B)  $\{ \ell l 22.8 \leq \ell \leq 23.4 \}$ 
C)  $\{ \ell \mid 23.4 \leq \ell \leq 23.7 \}$ 
D)  $\{$ ll $l \leq 23.4$ or $\ell \geq 23.7 \}$ 
A)  $\{ \ell l \ell \leq 22.8$ or $\ell \geq 23.4 \}$ 
B)  $\{ \ell l 22.8 \leq \ell \leq 23.4 \}$ 
C)  $\{ \ell \mid 23.4 \leq \ell \leq 23.7 \}$ 
D)  $\{$ ll $l \leq 23.4$ or $\ell \geq 23.7 \}$

Question 5

Solve the linear inequality. Other than Ø, graph the solution set on a number line.
-$$4 ( x + 7 ) \geq 3 ( x - 6 ) + x$$

Accepted Answer

A)  $( x , \infty )$
  
B)  $\varnothing$ 
C)  $[ 3 , \infty )$
  
D)  $( \infty , 3 ]$
  
A)  $( x , \infty )$
  
B)  $\varnothing$ 
C)  $[ 3 , \infty )$
  
D)  $( \infty , 3 ]$

Question 6

Solve the inequality. Other than Ø, graph the solution set on a number line.
-$$\frac { x - 3 } { 9 } \geq \frac { x - 5 } { 12 } + \frac { 1 } { 36 }$$

Accepted Answer

A)  $( - \infty , - 2 ]$
  
B)  $( - \infty , - 2 )$
  
C)  $[ - 2 , \infty )$
  
D)  $( - 2 , \infty )$
  
A)  $( - \infty , - 2 ]$
  
B)  $( - \infty , - 2 )$
  
C)  $[ - 2 , \infty )$
  
D)  $( - 2 , \infty )$

Question 7

Graph the inequality.
-$y \leq 4 x+4$

Accepted Answer

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

Question 8

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations.
-$|x-3|<0$

Accepted Answer

A)  $( - \infty , 3 )$
  
B)  $( - 3 , \infty )$
  
C) 
$\varnothing$ 
D) $( - 3,3 )$
  
A)  $( - \infty , 3 )$
  
B)  $( - 3 , \infty )$
  
C) 
$\varnothing$ 
D) $( - 3,3 )$

Question 9

Graph the inequality.
-$$4 x + y > - 4$$

Accepted Answer

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

Question 10

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations.
-$| x - 5 | \geq 0$

Accepted Answer

A)  $\{ 5 \}$
  
B) $( - 5,5 )$
  
C) $( 5 , \infty )$
  
D) $( - \infty , \infty )$
  
A)  $\{ 5 \}$
  
B) $( - 5,5 )$
  
C) $( 5 , \infty )$
  
D) $( - \infty , \infty )$

Question 11

Solve the inequality. Other than Ø, graph the solution set on a number line.
-$$\frac { x } { 3 } \geq 4 + \frac { x } { 15 }$$

Accepted Answer

A)  $( - \infty , 15 ]$
  
B)  $[ 15 , \infty )$
  
C)  $[ - 15 , \infty )$
  
D)  $( 15 , \infty )$
  
A)  $( - \infty , 15 ]$
  
B)  $[ 15 , \infty )$
  
C)  $[ - 15 , \infty )$
  
D)  $( 15 , \infty )$

Question 12

Find the union of the sets.
-{-5, -2, 1, 4} ∪ {1, 4, 7}

Accepted Answer

A)  {1, 4} 
B)  {1, 4, 7} 
C)  {-5, -2, 1, 4} 
D)  {-5, -2, 1, 4, 7} 
A)  {1, 4} 
B)  {1, 4, 7} 
C)  {-5, -2, 1, 4} 
D)  {-5, -2, 1, 4, 7}

Question 13

Solve the linear inequality. Other than Ø, graph the solution set on a number line.
-$$5 ( 4 x + 5 ) - 4 x < 4 ( 6 + 4 x ) - 6$$

Accepted Answer

A)  $( \infty , 5 )$
  
B)  $\varnothing$ 
C)  $( \infty , \infty )$
  
D)  $( 5 , \infty )$
  
A)  $( \infty , 5 )$
  
B)  $\varnothing$ 
C)  $( \infty , \infty )$
  
D)  $( 5 , \infty )$

Question 14

Find the solution set for the equation.
-$$3 | x - 3 | = 18$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ 3 \}$ 
C)  $\{ 9 , - 3 \}$ 
D)  $\{ 3 , - 9 \}$ 
A)  $\varnothing$ 
B)  $\{ 3 \}$ 
C)  $\{ 9 , - 3 \}$ 
D)  $\{ 3 , - 9 \}$

Question 15

Find the intersection of the sets.
-$\{ a , e , o , u \} \cap \varnothing$

Accepted Answer

A)  $\{ a \}$ 
B)  $\varnothing$ 
C)  $\{ \mathrm { u } \}$ 
D)  $\{ a , e , o , u \}$ 
A)  $\{ a \}$ 
B)  $\varnothing$ 
C)  $\{ \mathrm { u } \}$ 
D)  $\{ a , e , o , u \}$

Question 16

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
-$x \leq 1$ anc $x \geq - 2$

Accepted Answer

A) $\phi$ 
B)  $( - \infty , - 2 ] \cup [ 1 , \infty )$
  
C) $[ - 2,1 ]$
  
D)  $( - 2,1 )$
  
A) $\phi$ 
B)  $( - \infty , - 2 ] \cup [ 1 , \infty )$
  
C) $[ - 2,1 ]$
  
D)  $( - 2,1 )$

Question 17

Solve and graph the solution set on a number line.
-$$| x | > 6$$

Accepted Answer

A)  $( - 6,6 )$
  
B)  $( - \infty , - 6 ) \cup ( 6 , \infty )$
  
C)  $( - \infty , - 6 ] \cup [ 6 , \infty )$
  
D)  $[ - 6,6 ]$
  
A)  $( - 6,6 )$
  
B)  $( - \infty , - 6 ) \cup ( 6 , \infty )$
  
C)  $( - \infty , - 6 ] \cup [ 6 , \infty )$
  
D)  $[ - 6,6 ]$

Question 18

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
-$x < 4$ or $x < 8$

Accepted Answer

A)  $( - \infty , 4 )$
  
B)  $( 4,8 )$ 
C)  
$( - \infty , 4 ) \cup ( 8 , \infty )$
  
D)  $( - \infty , 8 )$
  
A)  $( - \infty , 4 )$
  
B)  $( 4,8 )$ 
C)  
$( - \infty , 4 ) \cup ( 8 , \infty )$
  
D)  $( - \infty , 8 )$

Question 19

Graph the inequality.
-

Accepted Answer

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

Question 20

Graph the inequality.
-$$y > 2 x - 4$$

Accepted Answer

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

Solve the inequality. Other than Ø, graph the solution set on a number line. - $- 6 x + 8 - 4 x < 8 - 12 x + 6$

Solve and graph the solution set on a number line. - $| 3 ( x + 1 ) + 9 | \geq 15$ $Solve and graph the solution set on a number line. - | 3 ( x + 1 ) + 9 | \geq 15$

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - $4 x < 12$ and $x + 4 > 5$

Solve. -The length ℓ of a metal rod used in manufacturing cars must not differ from the standard s by more than 0.3 inches. The manufacturing engineers express this as |ℓ- s| ≤0.3. If the standard s is 23.1, solve the inequality for the length ℓ. Express the answer in set-builder notation.

Solve the linear inequality. Other than Ø, graph the solution set on a number line. - $4 ( x + 7 ) \geq 3 ( x - 6 ) + x$ $Solve the linear inequality. Other than Ø, graph the solution set on a number line. - 4 ( x + 7 ) \geq 3 ( x - 6 ) + x$

Graph the inequality. - $y \leq 4 x+4$ $Graph the inequality. - y \leq 4 x+4$

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations. - $|x-3|<0$

Graph the inequality. - $4 x + y > - 4$

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations. - $| x - 5 | \geq 0$ $Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations. - | x - 5 | \geq 0$

Solve the inequality. Other than Ø, graph the solution set on a number line. - $\frac { x } { 3 } \geq 4 + \frac { x } { 15 }$ $Solve the inequality. Other than Ø, graph the solution set on a number line. - \frac { x } { 3 } \geq 4 + \frac { x } { 15 }$

Find the union of the sets. -{-5, -2, 1, 4} ∪ {1, 4, 7}

Solve the linear inequality. Other than Ø, graph the solution set on a number line. - $5 ( 4 x + 5 ) - 4 x < 4 ( 6 + 4 x ) - 6$

Find the solution set for the equation. - $3 | x - 3 | = 18$

Find the intersection of the sets. - $\{ a , e , o , u \} \cap \varnothing$

Solve and graph the solution set on a number line. - $| x | > 6$

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - $x < 4$ or $x < 8$

Graph the inequality. -

Graph the inequality. - $y > 2 x - 4$

Algebra, Mathematical Models, and Problem Solving

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Polynomials, Polynomial Functions, and Factoring

Rational Expressions, Functions, and Equations

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Exam 4: Inequalities and Problem Solving

Solve the inequality. Other than Ø, graph the solution set on a number line. - −6x+8−4x<8−12x+6- 6 x + 8 - 4 x < 8 - 12 x + 6−6x+8−4x<8−12x+6

Solve and graph the solution set on a number line. - ∣3(x+1)+9∣≥15| 3 ( x + 1 ) + 9 | \geq 15∣3(x+1)+9∣≥15

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - 4x<124 x < 124x<12 and x+4>5x + 4 > 5x+4>5

Solve. -The length ℓ of a metal rod used in manufacturing cars must not differ from the standard s by more than 0.3 inches. The manufacturing engineers express this as |ℓ- s| ≤0.3. If the standard s is 23.1, solve the inequality for the length ℓ. Express the answer in set-builder notation.

Solve the linear inequality. Other than Ø, graph the solution set on a number line. - 4(x+7)≥3(x−6)+x4 ( x + 7 ) \geq 3 ( x - 6 ) + x4(x+7)≥3(x−6)+x

Solve the inequality. Other than Ø, graph the solution set on a number line. - x−39≥x−512+136\frac { x - 3 } { 9 } \geq \frac { x - 5 } { 12 } + \frac { 1 } { 36 }9x−3​≥12x−5​+361​

Graph the inequality. - y≤4x+4y \leq 4 x+4y≤4x+4

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations. - ∣x−3∣<0|x-3|<0∣x−3∣<0

Graph the inequality. - 4x+y>−44 x + y > - 44x+y>−4

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations. - ∣x−5∣≥0| x - 5 | \geq 0∣x−5∣≥0

Solve the inequality. Other than Ø, graph the solution set on a number line. - x3≥4+x15\frac { x } { 3 } \geq 4 + \frac { x } { 15 }3x​≥4+15x​

Find the union of the sets. -{-5, -2, 1, 4} ∪ {1, 4, 7}

Solve the linear inequality. Other than Ø, graph the solution set on a number line. - 5(4x+5)−4x<4(6+4x)−65 ( 4 x + 5 ) - 4 x < 4 ( 6 + 4 x ) - 65(4x+5)−4x<4(6+4x)−6

Find the solution set for the equation. - 3∣x−3∣=183 | x - 3 | = 183∣x−3∣=18

Find the intersection of the sets. - {a,e,o,u}∩∅\{ a , e , o , u \} \cap \varnothing{a,e,o,u}∩∅

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - x≤1x \leq 1x≤1 anc x≥−2x \geq - 2x≥−2

Solve and graph the solution set on a number line. - ∣x∣>6| x | > 6∣x∣>6

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - x<4x < 4x<4 or x<8x < 8x<8

Graph the inequality. -

Graph the inequality. - y>2x−4y > 2 x - 4y>2x−4

Algebra, Mathematical Models, and Problem Solving

Functions and Linear Functions

Systems of Linear Equations

Polynomials, Polynomial Functions, and Factoring

Rational Expressions, Functions, and Equations

Radicals, Radical Functions, and Rational Exponents

Quadratic Equations and Functions

Filters

Solve the inequality. Other than Ø, graph the solution set on a number line. - $- 6 x + 8 - 4 x < 8 - 12 x + 6$

Solve and graph the solution set on a number line. - $| 3 ( x + 1 ) + 9 | \geq 15$ $Solve and graph the solution set on a number line. - | 3 ( x + 1 ) + 9 | \geq 15$

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - $4 x < 12$ and $x + 4 > 5$

Solve the linear inequality. Other than Ø, graph the solution set on a number line. - $4 ( x + 7 ) \geq 3 ( x - 6 ) + x$ $Solve the linear inequality. Other than Ø, graph the solution set on a number line. - 4 ( x + 7 ) \geq 3 ( x - 6 ) + x$

Graph the inequality. - $y \leq 4 x+4$ $Graph the inequality. - y \leq 4 x+4$

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations. - $|x-3|<0$

Graph the inequality. - $4 x + y > - 4$

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations. - $| x - 5 | \geq 0$ $Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations. - | x - 5 | \geq 0$

Solve the inequality. Other than Ø, graph the solution set on a number line. - $\frac { x } { 3 } \geq 4 + \frac { x } { 15 }$ $Solve the inequality. Other than Ø, graph the solution set on a number line. - \frac { x } { 3 } \geq 4 + \frac { x } { 15 }$

Solve the linear inequality. Other than Ø, graph the solution set on a number line. - $5 ( 4 x + 5 ) - 4 x < 4 ( 6 + 4 x ) - 6$

Find the solution set for the equation. - $3 | x - 3 | = 18$

Find the intersection of the sets. - $\{ a , e , o , u \} \cap \varnothing$

Solve and graph the solution set on a number line. - $| x | > 6$

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation. - $x < 4$ or $x < 8$

Graph the inequality. - $y > 2 x - 4$