Question

How do you solve and graph `2/3(x-12)≤x+12`?

Answer 1

`x>=-60`

Explanation:

Given:

`2/3(x-12)<=x+12`

Multiple both sides by `3`.

`2(x-12)<=3(x+12)`

Expand both sides.

`2x-24<=3x+36`

Subtract `2x` from
both sides.

`-24<=3x+36-2x`

Simplify.

`-24<=x+36`

Subtract `36` from both sides.

`-36-24<=x`

Simplify.

`-60<=x`

Switch sides.

`x>=-60`

The graph is a solid vertical line starting at `x=-60`. The solid line indicates that the graph is equal to `x=-60`. The inequality is represented by shading the graph from `x=-60` to infinity.

graph{x>=-60 [-69.35, -44.04, -2.29, 10.37]}