Question

Solve the following compound inequality: −2(x + 4) + 10 < x − 7 OR −2x + 9 > 3(x + 8)

A: x < 3 or x > −3
B: x > 3 or x < −3
C: x < 7 or x > −3
D: x > 7 or x < −3

Answer 1

#1

`\\ \sf{:}\!\implies -2(x+4)+10<x-7`

`\\ \sf{:}\!\implies -2x-8+10<x-7`

`\\ \sf{:}\!\implies x+2x>2+7`

`\\ \sf{:}\!\implies 3x>9`

`\\ \sf{:}\!\implies x>(9)/(3)`

`\\ \sf{:}\!\implies x>3`

#2

`\\ \sf{:}\!\implies -2x+9>3(x+8)`

`\\ \sf{:}\!\implies -2x+9>3x+24`

`\\ \sf{:}\!\implies -2x-3x>24-9`

`\\ \sf{:}\!\implies -5x>15`

`\\ \sf{:}\!\implies x>(15)/(-5)`

`\\ \sf{:}\!\implies x>-3`