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`

Answer 2

Answer B is correct

Explanation:

`1) - 2(x + 4) + 10 < x - 7 \\ - 2x - 8 + 10 < x - 7 \\ - 2x - x - 8 + 10 < - 7 \\ - 3x + 2 < - 7 \\ - 3x < - 7 - 2 \\ - 3x < - 9 \\ ( - 3x)/( - 3) < ( - 9)/( - 3) \\ x > 3`

`2) - 2x + 9 > 3(x + 8) \\ - 2x + 9 > 3x + 24\\ - 2x - 3x > - 9 + 24\\ - 5x > 15 \\ ( - 5x)/( - 5) > (15)/( - 5) \\ x < - 3`

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