Question

How do you graph `1/2x+8<=3`?

Answer 1

See a solution process below:

Explanation:

First, solve the inequality for `x`:

Subtract `color(red)(8)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`1/2x + 8 - color(red)(8) <= 3 - color(red)(8)`

`1/2x + 0 <= -5`

`1/2x <= -5`

Multiply each side of the inequality by `color(red)(2)` to solve for `x` while keeping the inequality balanced:

`color(red)(2) xx 1/2x <= color(red)(2) xx -5`

`cancel(color(red)(2)) xx 1/color(red)(cancel(color(black)(2)))x <= -10`

`x <= -10`

To graph this we will draw a vertical line at `-10` on the horizontal axis.

The line will be a solid line because the inequality operator contains an "or equal to" clause.

We will shade to the left side of the line because the inequality operator also contains a "less than" clause:

graph{x <= -10 [-20, 20, -10, 10]}