# How do you solve the inequality 7x – 2<3(3x + 2) ?

May 14, 2018

$x > 4$

#### Explanation:

$7 x - 2 < 3 \left(3 x + 2\right)$

First, use the distributive property to simplify $\textcolor{b l u e}{3 \left(3 x + 2\right)}$:

$\textcolor{b l u e}{3 \left(3 x + 2\right) = \left(3 \cdot 3 x\right) + \left(3 \cdot 2\right) = 9 x + 6}$

Now put that back into the inequality:
$7 x - 2 < 9 x + 6$

Subtract $\textcolor{b l u e}{6}$ from both sides of the inequality:
$7 x - 2 \quad \textcolor{b l u e}{- \quad 6} < 9 x + 6 \quad \textcolor{b l u e}{- \quad 6}$

$7 x - 8 < 9 x$

Subtract $\textcolor{b l u e}{7 x}$ from both sides of the inequality:
$7 x - 8 \quad \textcolor{b l u e}{- \quad 7 x} < 9 x \quad \textcolor{b l u e}{- \quad 7 x}$

$- 8 < 2 x$

Divide both sides by $\textcolor{b l u e}{2}$:
$- \frac{8}{\textcolor{b l u e}{2}} < \frac{2 x}{\textcolor{b l u e}{2}}$

$4 < x$

This can be read as "4 is less than x".

Since we want the variable on the left side, it becomes "x is more than 4, or:

$x > 4$

Hope this helps!