# How do you solve and graph 2(-3m - 5) ≥ -28 ?

Apr 2, 2017

$m \le 3$

#### Explanation:

Manipulate the inequality as you would an equation. However there is a trap when doing so. If you multiply by negative one then you turn the inequality round the other way. I will show you why in the explanation.

Given:$\text{ "2(-3m-5)>=-28" } \ldots \ldots \ldots \ldots . E q u a t i o n \left(1\right)$

Divide both sides by 2 (gets rid of the 2 on the left)

$- 3 m - 5 \ge - 14$

Add 5 to both sides (gets rid of the 5 on the left)

$- 3 m \ge - 9$

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Method 1:

$- 3 m \ge - 9$

Multiply both sides by (-1)

$\textcolor{m a \ge n t a}{+ 3 m \le + 9} \text{ } \ldots . . E q u a t i o n \left(2\right)$
......................................................................
Method 2:

$- 3 m \ge - 9$

Add $3 m$ to both sides

$0 \ge 3 m - 9$

$+ 9 \ge + 3 m$

Write as:

$\textcolor{m a \ge n t a}{3 m \le + 9} \text{ } \ldots \ldots \ldots \ldots E q u a t i o n \left(3\right)$
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Notice that both $E q u a t i o n \left(2\right) \mathmr{and} E q u a t i o n \left(3\right)$ are the same
This demonstrates why you turn the inequality round the other way when you multiply by negative one

$3 m \le 9$

Divide both sides by 3

$m \le 3$