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

Aug 28, 2015

#### Answer:

$x < - 19$

#### Explanation:

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

First, multiply the right-hand side of the inequality by $1 = \frac{4}{4}$

$\frac{3 \left(x - 5\right)}{4} > \left(x + 1\right) \cdot \frac{4}{4}$

This is equivalent to

$3 \left(x - 5\right) > 4 \left(x + 1\right)$

Use the distributive property of multiplication to break up those parantheses

$3 \cdot x - 3 \cdot 5 > 4 \cdot x + 4 \cdot 1$

$3 x - 15 > 4 x + 4$

This is equivalent to

$3 x - 4 x > 4 + 15$

$- x > 19$

Finally, multiply both sides by $\left(- 1\right)$ - 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]}