Question

HELP 50 PTS Solve the following compound inequality: −2(x + 4) + 10 < x − 7 or −2x + 9 > 3(x + 8)

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

• x > 3 or x < - 3

Given equations:

• −2(x + 4) + 10 < x − 7

or

• −2x + 9 > 3(x + 8)

Solve each inequality:

• −2(x + 4) + 10 < x − 7
• -2x - 8 + 10 < x - 7
• -2x - x < -7 - 2
• -3x < -9
• 3x > 9
• x > 3

or

• −2x + 9 > 3(x + 8)
• -2x + 9 > 3x + 24
• -2x - 3x > 24 - 9
• -5x > 15
• 5x < -15
• x < - 3