# How do you solve and graph 3[4x-(2x-7)]<2(3x-5)?

Jun 28, 2016

$x \in \emptyset$
That is there is no value of $x$ for which the given inequality is true.

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} 3 \left[4 x - \left(2 x - 7\right)\right] < 2 \left(3 x - 5\right)$

First, simplify both the left and right sides:
$\textcolor{w h i t e}{\text{XXX}} 3 \left[2 x + 7\right] < 6 x - 10$

$\textcolor{w h i t e}{\text{XXX}} 6 x + 21 < 6 x - 10$

Since we can subtract the same amount from both sides without effecting the validity or orientation of the inequality we have
$\textcolor{w h i t e}{\text{XXX}} 21 < - 10$

which is clearly not true for any value of $x$