Question

Solve the following absolute value inequality

Answer 1

x < -1

x > -13

Explanation:

Hello!

First, isolate the absolute value bracket:

• 
  `$(4|x + 7|)/(3) < 8$`
• 
  `4|x + 7| < 24`
• 
  `|x + 7| < 6`

Use the absolute value inequality rule:

`|x| < y \text {, if y is} \geq 0:\\-y < x < y`

Solve for x

• 
  `|x + 7| < 6`
• 
  `-6 < x + 7 < 6`
• 
  `-6 - 7 < x < 6 - 7`
• 
  `-13 < x < -1`

The solution is:

• x < -1
• x > -13

Answer 2

x < -1

x > -13

Explanation:

`(4|x+7|)/(3)<8`

`\implies 4|x+7|<24`

`\implies |x+7|<6`

`\textsf{Therefore} \ \ x+7<6 \ \ \textsf{and} \ -(x+7)<6`

`x+7<6`

`\implies x<-1`

`-(x+7)<6`

`\implies -x-7<6`

`\implies -x<13`

`\implies x > -13`