Question

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

Answer 1

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:
`2x-1 > 5 " and " 3x < -6`

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

`2x > 6` so `x>3`

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

`x < -2`

In order to satisfy the compound inequality:
`2x-1 > 5 " and " 3x < -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.