Absolute Value Equations and Inequalities Worksheet

Absolute Value Equations and Inequalities Worksheet
  • Page 1
 1.  
Solve the inequality, | 9 - x | < 5.
a.
{ x: 4 < x < 14 }
b.
{ x: x < 4 or x > 14 }
c.
{ x: x < - 14 or x > 4 }
d.
{ x: - 14 < x < 4 }


Answer: (a)


Correct answer : (1)
 2.  
Solve the inequality, | x - 3 | > 4.
a.
{ x: x < 1 or x > 7 }
b.
{ x: x < - 7 or x > 1 }
c.
{ x: x < -1 or x > 7 }
d.
None of the above


Answer: (c)


Correct answer : (3)
 3.  
Solve the inequality, | x + 2 | - 3 < 5.
a.
{ x: - 10 < x < 6 }
b.
{ x: 6 < x < 10 }
c.
{ x: - 10 < x < - 6 }
d.
{ x: - 2 < x < 8 }


Answer: (a)


Correct answer : (1)
 4.  
Solve the inequality, | 2x | < 16.
a.
{ x: - 8 ≤ x ≤ 8 }
b.
{ x: - 8 < x < 8 }
c.
{ x: 0 < x < 8 }
d.
{ x: - 8 < x < 0 }


Answer: (b)


Correct answer : (2)
 5.  
Solve the inequality, | x | + 3 < 10.
a.
{ x: - 7 < x < 7 }
b.
{ x: - 13 < x < 13 }
c.
{ x: 7 < x < 13 }
d.
None of the above


Answer: (a)


Correct answer : (1)
 6.  
Solution for the inequality is given in set-builder notation. Solve and choose the correct one for the inequality given.
3[2y + (3y - 1)] ≥ 5(2y + 1)
a.
{y: y ≤ 1.6}
b.
{y: y ≥ 1.6}
c.
{y: y ≤ - 1.6}
d.
{y: y ≥ 2.6}


Answer: (b)


Correct answer : (2)
 7.  
Identify the graph that the inequality represents.

7r - 9 < 4r + 30


a.
Graph A
b.
Graph B
c.
Graph C
d.
Graph D


Answer: (b)


Correct answer : (2)
 8.  
Solve for x.
5ax + 8b < 2ax - 6b, a < 0
a.
{x: x > 14b3a }
b.
{x: x > - 14b3a }
c.
{x: x < 14b3a }
d.
{x: x < - 14b3a }


Answer: (b)


Correct answer : (2)
 9.  
Solution for the inequality is given in set-builder notation. Solve and choose the correct one for the inequality given.
7 [2x - (x + 7)] < 3 (2x - 3)
a.
{x: x < - 40}
b.
{x: x < - 58}
c.
{x: x < 58}
d.
{x: x < 40}


Answer: (d)


Correct answer : (4)
 10.  
Solve and identify the graph that represents the inequality.
15 < 3 (2n + 1) + 24, n is a real number.

a.
n < - 2, Graph A
b.
n > - 2, Graph B
c.
n ≥ - 2, Graph C
d.
n ≤ - 2, Graph D


Answer: (b)


Correct answer : (2)

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