Question

How do you graph `7/3x <7`?

Answer 1

See a solution process below:

Explanation:

Multiply each side of the inequality by `color(red)(3)/color(blue)(7)` to solve for `x` while keeping the inequality balanced:

`color(red)(3)/color(blue)(7) xx 7/3x < color(red)(3)/color(blue)(7) xx 7`

`cancel(color(red)(3))/cancel(color(blue)(7)) xx color(blue)(cancel(color(black)(7)))/color(red)(cancel(color(black)(3)))x < color(red)(3)/cancel(color(blue)(7)) xx color(blue)(cancel(color(black)(7)))`

`x < 3`

To graph this we will draw a vertical line at `3` on the horizontal axis.

The line will be a dashed line because the inequality operator does not contain an "or equal to" clause.

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

graph{x < 3 [-10, 10, -5, 5]}