# How do you solve the inequality -3x< -6 or x + 5<= -2 ?

May 18, 2017

See explanation

#### Explanation:

Given:

$- 3 x < - 6 \text{ } \ldots \ldots \ldots \ldots . E q u a t i o n \left(1\right)$
$x + 5 \le - 2 \text{ } \ldots \ldots \ldots \ldots E q u a t i o n \left(2\right)$

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$\textcolor{b l u e}{\text{Consider } E q u a t i o n \left(1\right)}$

Multiply both sides by (-1) to make the $x$ term positive.

This action reverses the inequality sign as well as changing the signs.:

$+ 3 x > + 6$

Divide both sides by 3

$x > \frac{6}{3}$

$\textcolor{g r e e n}{x > 2 \text{ } \ldots \ldots \ldots \ldots \ldots . E q u a t i o n \left({1}_{a}\right)}$

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$\textcolor{b l u e}{\text{Consider } E q u a t i o n \left(2\right)}$

Subtract 5 from both sides

$\textcolor{g r e e n}{x \le - 7 \text{ } \ldots \ldots \ldots \ldots \ldots \ldots . E q u a t i o n \left({2}_{a}\right)}$
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If you were to combine these you would have

$2 < x \le - 7$