Question

How do you solve `2x+3(x-2)>=x+2`?

Answer 1

`x>=2`

Explanation:

Solve:

`2x+3(x-2)>=x+2`

Expand.

`2x+3x-6>=x+2`

Subtract `x` from both sides.

`2x+3x-x-6>=2`

Add `6` to both sides.

`2x+3x-x-6+6>=x-x+2+6`

Simplify.

`2x+3x-x-color(red)cancel(color(black)(6))+color(red)cancel(color(black)(6))>=color(red)cancel(color(black)(x))-color(red)cancel(color(black)(x))+2+6`

`4x>=8`

Divide both sides by `4`.

`(color(red)cancel(color(black)(4))x)/color(red)cancel(color(black)(4))>=color(red)cancel(color(black)(8))^color(blue)2/color(red)cancel(color(black)(4))^color(blue)1`

`x>=2`