Question

How do you solve and graph `12 + x ≤ 9`?

Answer 1

See a solution process below:

Explanation:

Subtract `color(red)(12)` from each side of the inequality to solve for `x` while keeping the equation balanced:

`-color(red)(12) + 12 + x <= -color(red)(12) + 9`

`0 + x <= -3`

`x <= -3`

To graph we draw a solid, vertical line at the point `-3` on the `x-axis` and shade to the left of the line.

We use a solid line because the inequality contains "or equal to". If the inequality was just "less than" we would use a dashed line.

We shade to the left of the line because the inequality is a "less" inequality.

graph{x <= - 3}