Question 1

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations.
-$$| 3 x - 3 | + 7 < - 1$$

Accepted Answer

A)  $\varnothing$
  
B)  $\left( - \infty , - \frac { 5 } { 3 } \right)$
  
C)  $\left( - \infty , \frac { 11 } { 3 } \right)$
  
D)  $\left( - \frac { 5 } { 3 } , \frac { 11 } { 3 } \right)$
  
A)  $\varnothing$
  
B)  $\left( - \infty , - \frac { 5 } { 3 } \right)$
  
C)  $\left( - \infty , \frac { 11 } { 3 } \right)$
  
D)  $\left( - \frac { 5 } { 3 } , \frac { 11 } { 3 } \right)$
  A

Question 2

Graph the inequality.
-

Accepted Answer

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

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.
-$x+6<3 \text { and }-6 x<-6$

Accepted Answer

A) 
$\phi$ 
B)  $( - \infty , - 3 )$
  
C) $( - 3,1 )$
  
D)  $( - \infty , - 3 ) \cup ( 1 , \infty )$
  
A) 
$\phi$ 
B)  $( - \infty , - 3 )$
  
C) $( - 3,1 )$
  
D)  $( - \infty , - 3 ) \cup ( 1 , \infty )$
  A

Question 4

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

Accepted Answer

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

Question 5

Solve and graph the solution set on a number line.
-$| 7 x + 9 | + 1 < 7$

Accepted Answer

A)  $\left( - \infty , - \frac { 15 } { 7 } \right)$
  
B)  $\left( - \frac { 3 } { 7 } , - \frac { 15 } { 7 } \right)$
  
C) $ \left( - \frac { 15 } { 7 } , - \frac { 3 } { 7 } \right)$
  
D)   
A)  $\left( - \infty , - \frac { 15 } { 7 } \right)$
  
B)  $\left( - \frac { 3 } { 7 } , - \frac { 15 } { 7 } \right)$
  
C) $ \left( - \frac { 15 } { 7 } , - \frac { 3 } { 7 } \right)$
  
D)

Question 6

Graph the inequality.
-$$\frac { x } { 5 } + \frac { y } { 2 } > 1$$

Accepted Answer

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

Question 7

Solve.
-A certain store has a fax machine available for use by its customers. The store charges $2.00 to send the first page and $0.50 for each subsequent page. Use an inequality to find the number of pages that can be faxed for $6.00.

Accepted Answer

A)  3 pages or fewer 
B)  9 pages or fewer 
C)  12 pages or fewer 
D)  48 pages or fewer 
A)  3 pages or fewer 
B)  9 pages or fewer 
C)  12 pages or fewer 
D)  48 pages or fewer

Question 8

Find the solution set for the equation.
-$$| x - 5 | = 4$$

Accepted Answer

A)  $\varnothing$ 
B)  $\{ 1,9 \}$ 
C)  $\{ - 9 \}$ 
D)  $\{ - 1,9 \}$ 
A)  $\varnothing$ 
B)  $\{ 1,9 \}$ 
C)  $\{ - 9 \}$ 
D)  $\{ - 1,9 \}$

Question 9

Solve the inequality. Other than Ø, graph the solution set on a number line.
-$$\frac { x } { 6 } - \frac { 1 } { 4 } \leq \frac { x } { 3 } + 2$$

Accepted Answer

A)  $\left[ - \frac { 27 } { 2 } , \infty \right)$
  
B)  $\left( * , - \frac { 27 } { 2 } \right)$
  
C)  $\left[ \infty , - \frac { 27 } { 2 } \right]$
  
D)  $\left( - \frac { 27 } { 2 } , \infty \right)$
  
A)  $\left[ - \frac { 27 } { 2 } , \infty \right)$
  
B)  $\left( * , - \frac { 27 } { 2 } \right)$
  
C)  $\left[ \infty , - \frac { 27 } { 2 } \right]$
  
D)  $\left( - \frac { 27 } { 2 } , \infty \right)$

Question 10

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.
-$x \leq 4 { } ^ { A } x \geq 8$

Accepted Answer

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

Question 11

Solve.
-Every Sunday, Jarod buys a loaf of fresh bread for his family from the corner bakery for $2.00. The local department store has a sale on breadmakers for $83. If the bread-making supplies cost $0.93 per week, for how many weeks would Jarod have to bake a loaf of bread at home before the breadmaker starts saving him money?

Accepted Answer

A)  At least 80 weeks 
B)  At least 77 weeks 
C)  At least 78 weeks 
D)  At least 79 weeks 
A)  At least 80 weeks 
B)  At least 77 weeks 
C)  At least 78 weeks 
D)  At least 79 weeks

Question 12

Solve and graph the solution set on a number line.
-$| x - 9 | > 9$

Accepted Answer

A)  $[ 0,18 ]$
  
B)  $( 0,18 )$
  
C) $( - \infty , 0 ) \cup ( 18 , \infty )$
  
D) 
$\varnothing$ 
A)  $[ 0,18 ]$
  
B)  $( 0,18 )$
  
C) $( - \infty , 0 ) \cup ( 18 , \infty )$
  
D) 
$\varnothing$

Question 13

Graph the inequality.
-$$y < - \frac { 2 } { 5 } x$$

Accepted Answer

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

Question 14

Solve.
-A landscaping company sells 40-pound bags of top soil. The actual weight x of a bag, however, may differ from the advertised weight by as much as 0.75 pound. Write an inequality involving absolute value that expresses the relationship between the actual weight x of a bag and 40 pounds. Solve the inequality, and express the answer in interval form.

Accepted Answer

A)  $| x + 0.75 | \leq 40 ; [ 39.25 , \infty )$ 
B)  $| 40 - \mathrm { x } | \leq 0.75 ; [ 39.25,40.75 ]$ 
C)  $| 40 + x | \leq 0.75 ; [ 39.25,40.75 ]$ 
D)    
A)  $| x + 0.75 | \leq 40 ; [ 39.25 , \infty )$ 
B)  $| 40 - \mathrm { x } | \leq 0.75 ; [ 39.25,40.75 ]$ 
C)  $| 40 + x | \leq 0.75 ; [ 39.25,40.75 ]$ 
D)

Question 15

Solve and graph the solution set on a number line.
-$| 2x - 9 | -4 \leq 4$

Accepted Answer

A) $[ \frac { 1 } { 2 }]  , \frac { 17 } { 2 }]$ 
B) $\text {  } \phi$ 
C) $[ \frac { 17 } { 2 }]  , \frac { 1 } { 2 }]$
  
D)    
A) $[ \frac { 1 } { 2 }]  , \frac { 17 } { 2 }]$ 
B) $\text {  } \phi$ 
C) $[ \frac { 17 } { 2 }]  , \frac { 1 } { 2 }]$
  
D)

Question 16

Solve the inequality. Other than Ø, graph the solution set on a number line.
-$$- 4 x \geq 24$$

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

Find the union of the sets.
-{-5, -1, 2, 6} ∪ {-3, 1, 4, 8}

Accepted Answer

A)  {-1, 1, 2} 
B)  {-5, -3, -1, 1, 2, 4, 6, 8} 
C)  {1} 
D)  Ø 
A)  {-1, 1, 2} 
B)  {-5, -3, -1, 1, 2, 4, 6, 8} 
C)  {1} 
D)  Ø

Question 19

Solve. Use interval notation to express the range.
-On the first four exams, your grades are 79, 89, 68, and 80. You are hoping to earn a C in the course. This will occur if the average of your five exam grades is greater than or equal to 70 and less than 80. What range of grades on the fifth exam will result in earning a C?

Accepted Answer

A)  (24, 74] 
B)  [34, 84) 
C)  (34, 84] 
D)  [24, 74) 
A)  (24, 74] 
B)  [34, 84) 
C)  (34, 84] 
D)  [24, 74)

Question 20

Solve. Use interval notation to express the range.
-The formula for converting Fahrenheit temperature, $F$, to Celsius temperature, $C$, is
$$C = \frac { 5 } { 9 } ( F - 32 ) \text {. }$$
If Celsius temperature ranges from $- 10 ^ { \circ }$ to $45 ^ { \circ }$, inclusive, what is the range for the Fahrenheit temperature?

Accepted Answer

A)  $[ 14,113 ]$ 
B)  $( - 19 , - 13 )$ 
C)  $( 14,113 )$ 
D)  $[ - 19 , - 13 ]$ 
A)  $[ 14,113 ]$ 
B)  $( - 19 , - 13 )$ 
C)  $( 14,113 )$ 
D)  $[ - 19 , - 13 ]$

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations. - $| 3 x - 3 | + 7 < - 1$

Graph the inequality. -

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

Solve and graph the solution set on a number line. - $| 7 x + 9 | + 1 < 7$

Graph the inequality. - $\frac { x } { 5 } + \frac { y } { 2 } > 1$ $Graph the inequality. - \frac { x } { 5 } + \frac { y } { 2 } > 1$

Solve. -A certain store has a fax machine available for use by its customers. The store charges $2.00 to send the first page and $0.50 for each subsequent page. Use an inequality to find the number of pages that can be faxed for $6.00.

Find the solution set for the equation. - $| x - 5 | = 4$

Solve the inequality. Other than Ø, graph the solution set on a number line. - $\frac { x } { 6 } - \frac { 1 } { 4 } \leq \frac { x } { 3 } + 2$ $Solve the inequality. Other than Ø, graph the solution set on a number line. - \frac { x } { 6 } - \frac { 1 } { 4 } \leq \frac { x } { 3 } + 2$

Solve and graph the solution set on a number line. - $| x - 9 | > 9$

Graph the inequality. - $y < - \frac { 2 } { 5 } x$ $Graph the inequality. - y < - \frac { 2 } { 5 } x$

Solve and graph the solution set on a number line. - $| 2x - 9 | -4 \leq 4$ $Solve and graph the solution set on a number line. - | 2x - 9 | -4 \leq 4$

Solve the inequality. Other than Ø, graph the solution set on a number line. - $- 4 x \geq 24$ $Solve the inequality. Other than Ø, graph the solution set on a number line. - - 4 x \geq 24$

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

Find the union of the sets. -{-5, -1, 2, 6} ∪ {-3, 1, 4, 8}

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

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Exam 4: Inequalities and Problem Solving

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations. - ∣3x−3∣+7<−1| 3 x - 3 | + 7 < - 1∣3x−3∣+7<−1

Graph the inequality. -

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+6<3 and −6x<−6x+6<3 \text { and }-6 x<-6x+6<3 and −6x<−6

Solve the linear inequality. Other than Ø, graph the solution set on a number line. - −5x≤−5(x−6)- 5 x \leq - 5 ( x - 6 )−5x≤−5(x−6)

Solve and graph the solution set on a number line. - ∣7x+9∣+1<7| 7 x + 9 | + 1 < 7∣7x+9∣+1<7

Graph the inequality. - x5+y2>1\frac { x } { 5 } + \frac { y } { 2 } > 15x​+2y​>1

Solve. -A certain store has a fax machine available for use by its customers. The store charges $2.00 to send the first page and $0.50 for each subsequent page. Use an inequality to find the number of pages that can be faxed for $6.00.

Find the solution set for the equation. - ∣x−5∣=4| x - 5 | = 4∣x−5∣=4

Solve the inequality. Other than Ø, graph the solution set on a number line. - x6−14≤x3+2\frac { x } { 6 } - \frac { 1 } { 4 } \leq \frac { x } { 3 } + 26x​−41​≤3x​+2

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≤4Ax≥8x \leq 4 { } ^ { A } x \geq 8x≤4Ax≥8

Solve and graph the solution set on a number line. - ∣x−9∣>9| x - 9 | > 9∣x−9∣>9

Graph the inequality. - y<−25xy < - \frac { 2 } { 5 } xy<−52​x

Solve and graph the solution set on a number line. - ∣2x−9∣−4≤4| 2x - 9 | -4 \leq 4∣2x−9∣−4≤4

Solve the inequality. Other than Ø, graph the solution set on a number line. - −4x≥24- 4 x \geq 24−4x≥24

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

Find the union of the sets. -{-5, -1, 2, 6} ∪ {-3, 1, 4, 8}

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 and graph the solution set on a number line. Express the solution set in both set-builder and interval notations. - $| 3 x - 3 | + 7 < - 1$

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

Solve and graph the solution set on a number line. - $| 7 x + 9 | + 1 < 7$

Graph the inequality. - $\frac { x } { 5 } + \frac { y } { 2 } > 1$ $Graph the inequality. - \frac { x } { 5 } + \frac { y } { 2 } > 1$

Find the solution set for the equation. - $| x - 5 | = 4$

Solve the inequality. Other than Ø, graph the solution set on a number line. - $\frac { x } { 6 } - \frac { 1 } { 4 } \leq \frac { x } { 3 } + 2$ $Solve the inequality. Other than Ø, graph the solution set on a number line. - \frac { x } { 6 } - \frac { 1 } { 4 } \leq \frac { x } { 3 } + 2$

Solve and graph the solution set on a number line. - $| x - 9 | > 9$

Graph the inequality. - $y < - \frac { 2 } { 5 } x$ $Graph the inequality. - y < - \frac { 2 } { 5 } x$

Solve and graph the solution set on a number line. - $| 2x - 9 | -4 \leq 4$ $Solve and graph the solution set on a number line. - | 2x - 9 | -4 \leq 4$

Solve the inequality. Other than Ø, graph the solution set on a number line. - $- 4 x \geq 24$ $Solve the inequality. Other than Ø, graph the solution set on a number line. - - 4 x \geq 24$

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