# How do you solve 2x - 1 > 5 and 3x < - 6?

##### 1 Answer
Jul 6, 2015

The compound inequality has no solution.

#### Explanation:

This is a Compound Inequality.

In order to solve an inequality that involves the word "and", we must find values of $x$ that make the inequalities true at the same time. (To solve a compound inequality with "or" we need to find values of $x$ that make at least one of the inequalities true.)

The problem asks us to solve:
$2 x - 1 > 5 \text{ and } 3 x < - 6$

In order to satisfy: $2 x - 1 > 5$ we need:

$2 x > 6$ so $x > 3$

In order to satisfy: $3 x < - 6$ we need:

$x < - 2$

In order to satisfy the compound inequality:
$2 x - 1 > 5 \text{ and } 3 x < - 6$

we need an $x$ that satisfies both:

$x > 3$ and the same $x$ satisfies $x < - 2$. There is no such $x$.

It may help to think of the number line. We need a number $x$ that is to the right of $3$ and the same number if to the left of $- 2$. No such number exists.