Question

How do you solve and graph `5x < 3 (x-4) + 7`?

Answer 1

For linear inequalities, you solve for x just as you would in an equation except you flip the inequality sign's direction if multiplying or dividing by a negative number.

Explanation:

`5x < 3x - 12 + 7`

`5x - 3x < -12 + 7`

`2x < -5`

`x < -5/2`

Since this is a single variable inequality, you will graph it on a number line. See the following diagram.

In the diagram, the black rectangle has been placed over the solution area (any numbers smaller than -2.5, for infinity).

Practice exercises:

1. Solve the following inequalities, and graph them on the number lines:

a) `2x - 3(x + 4) > 5x`

b) `3(2x + 4) + 2(2x - 6) < 4/(2(x - 1))`

Good luck!