Q37. - Algebra 2

Question

Solve  $\left|x+4\right|>3$

Step-by-Step Solution

Answer

The solution of the given inequality is $x\left\{\left.x\right|x<-7\right. or x>-\left.1\right\}$.

Step-1 &ndash; Compound inequality

A compound inequality is an equation with two or more inequalities joined together with either “and” or “or”.

Step-2 &ndash; Rewrite the given inequality.

$\begin{array}{l}\left|x+4\right|>3\\ x+4>3orx+4<-3\end{array},$

Step-3 &ndash; Subtract each part of both inequalities by 4.

$\begin{array}{l}x+4-4>3-4\\ x>-1\end{array}$

Or

$\begin{array}{l}x+4-4<-3-4\\ x>-7\end{array}$

So, the solution of the given inequality is $x\left\{\left.x\right|x<-7\right. or x>-\left.1\right\}$.