Question

How do you solve and graph `x/4<9`?

Answer 1

See a solution process below:

Explanation:

Multiply each side of the inequality by `color(red)(4)` to solve for `x` while keeping the inequality balanced:

`color(red)(4) xx x/4 < color(red)(4) xx 9`

`cancel(color(red)(4)) xx x/color(red)(cancel(color(black)(4))) < 36`

`x < 36`

To solve this we draw a vertical line at `36` on the `x` axis.

The line will be dashed because the inequality is just "less than" and does not contain an "or equal to" clause. Therefore the solution does not contain the point `36`.

We will shade to the left of the line because this is a "less than" inequality:

graph{x < 36 [-10, 40, -12.5, 12.5]}