How do you solve 4+ 2( x - 7) < - 18?

May 15, 2018

$x < - 4$

Explanation:

Solving inequalities is similar to solving equations.

First, use the distributive property to simplify $\textcolor{b l u e}{2 \left(x - 7\right)}$:
$\textcolor{b l u e}{2 \left(x - 7\right) = 2 x - 14}$

Put that back into the inequality:
$4 + 2 x - 14 < - 18$

Combine $\textcolor{b l u e}{4 - 14}$:

$- 10 + 2 x < - 18$

Add $\textcolor{b l u e}{10}$ to both sides:
$- 10 + 2 x \quad \textcolor{b l u e}{+ \quad 10} < - 18 \quad \textcolor{b l u e}{+ \quad 10}$

$2 x < - 8$

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

$x < - 4$

This can be said as "$x$ is less than $- 4$.

Hope this helps!