# How do you solve a-2<3a+2(a+3)?

Apr 18, 2016

$a > - 2$

#### Explanation:

Given:
$\textcolor{w h i t e}{\text{XXX}} a - 2 < 2 a + 2 \left(a + 3\right)$

Simplify the right side:
$\textcolor{w h i t e}{\text{XXX}} a - 2 < 3 a + 2 a + 6$

$\textcolor{w h i t e}{\text{XXX}} a - 2 < 5 a + 6$

Subtract $\left(a + 6\right)$ from both sides
$\textcolor{w h i t e}{\text{XXX}} - 8 < 4 a$

Divide both sides by $4$
$\textcolor{w h i t e}{\text{XXX")-2 < acolor(white)("XX")orcolor(white)("XX}} a > - 2$

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Remember:
When working with inequalities you can:
$\textcolor{w h i t e}{\text{XXX}}$add or subtract the same amount to both sides; and
$\textcolor{w h i t e}{\text{XXX}}$multiply or divide both sides by the same positive amount.
without changing the direction of the inequality sign.

If you multiply or divide both sides by an negative amount:
$\textcolor{w h i t e}{\text{XXX}}$the inequality sign must be reversed.