# How do you solve –2(x – 3) ≥ 5 – (x + 3)?

Mar 7, 2018

$x \le 4$

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} - 2 \left(x - 3\right) \ge 5 - \left(x + 3\right)$

Simplifying each side independently
$\textcolor{w h i t e}{\text{XXX}} - 2 x + 6 \ge 2 - x$

We could add $2 x$ to both sides (you can add any amount to both sides of an inequality without effecting its validity or direction)
$\textcolor{w h i t e}{\text{XXX}} 6 \ge 2 + x$

Then, if we subtract $2$ from both sides
$\textcolor{w h i t e}{\text{XXX}} 4 \ge x$...or, if you like your variables on the left
$\textcolor{w h i t e}{\text{XXX}} x \le 4$

Mar 7, 2018

See details below

#### Explanation:

First expand inequation removing braquets

$- 2 x + 6 \ge 5 - x - 3$. Now, adding to both sides in order to transpose terms, we have

$6 - 5 + 3 \ge - x + 2 x$ this is the same to

$4 \ge x$

The inequation has as solutions all numbers $x$ lower than $4$, it's say $\left(- \infty , 4\right]$