Question

How do you solve and graph `(3 ( x - 5 )) / 4 > x + 1`?

Answer 1

`x < -19`

Explanation:

Your goal here is to isolate `x` on one side of the inequality.

First, multiply the right-hand side of the inequality by `1= 4/4`

`(3(x-5))/4 > (x+1) * 4/4`

This is equivalent to

`3(x-5) > 4(x+1)`

Use the distributive property of multiplication to break up those parantheses

`3 * x - 3 * 5 > 4 * x + 4 * 1`

`3x - 15> 4x + 4`

This is equivalent to

`3x - 4x > 4 + 15`

`-x > 19`

Finally, multiply both sides by `(-1)` - don't forget to change the sign of the inequality!

`x < -19`

To graph this inequality, draw a dotted vertical line thorugh `x = -19` and shade the area to the left of the line, since you need values of `x` that are smaller than `-19`.

graph{x < -19 [-58.5, 58.54, -29.26, 29.3]}