Solving Absolute Value Inequalities

Solve.
|c + 4| < 5

• x < -9 or x > 1
• -9 < x < 1
• x < 9 or x > -1
• -1 < x < 9

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve.
|y - 4| ≥ 8

• y ≤ -4 or y ≥ 12
• -4 ≤ y ≤ -12
• y ≤ 4 or y ≥ -12
• -12 ≤ x ≤ 4

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

Solve.
|y - 1| ≤ 6

• -7 ≤ y ≤ 5
• y ≤ -7 or y ≥ 5
• -5 ≤ y ≤ 7
• y ≤ -5 or y ≥ 7

Solve:
|x + 3| > - 8

• x > 5 or x < -11
• x > 5
• all real numbers
• no solution

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve.

|3c - 4| < 12

• 
  

  $-\frac{8}{3}<c<\frac{16}{3}$

• $c<-\frac{16}{3}\ \ or\ \ \ c>\frac{8}{3}$
  

• $c\ <\frac{16}{3}\ \ or\ \ c\ >-\frac{8}{3}$

• $-\frac{16}{3}\ <\ c\ <\ \frac{8}{3}$
  

Solve.

 $\left|2t\ +\frac{2}{3}\right|\ <\ 4$  

•  $-\frac{5}{3}\ <\ t\ \ <\ \frac{7}{3}$  

•  $t\ <-\frac{5}{3}\ \ or\ \ t\ >\frac{7}{3}$  

•  $-\frac{7}{3}\ <\ t\ \ <\ \frac{5}{3}$ 

•  $t\ <-\frac{7}{3}\ \ or\ \ t\ >\frac{5}{3}$  

Solve.

|5x + 7| < 22

• $x<-\frac{29}{5}\ \ or\ \ \ x>3$

• $-\frac{29}{5}\ <\ x\ <\ 3$

• $-3\ <\ x\ <\frac{29}{5}\$

• $x\ >\frac{29}{5}\ \ or\ \ \ x<-3$

Solve.
|4k + 12| ≥ 6

• v ≤ -4.5 or v ≥ -1.5
• -4.5 ≤ v ≤ -1.4
• -1.5 ≤ v ≤ 4.5
• v ≤ -1.5 or v ≥ 4.5

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve.
|-3d| ≥ 6.3

• -18.9 ≤ f ≤ 18.9
• no solution
• f ≤ -2.1 or f ≥ 2.1
• -2.1 ≤ f ≤ 2.1

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Solve.

6 - 2|m - 3| > -4

• -8 < m < 2

• m < -8 or m > 2

• m < -2 or m > 8

• -2 < m < 8