Step 1

We need to solve the absolute value inequality.

\(\displaystyle{\left|{{2}{x}+{4}}\right|}{>}{6}\)

Step 2

Firstly we discuss the rules of absolute value inequalities.

Here the steps :

Step 1: Isolate the absolute value on left hand side.

Step 2: Remove the absolute value sign.

Step 3: For greater than sign:

Quantity inside the absolute value < - (Number on other side)

OR

Quantity inside the absolute value > (Number on other side)

Step 3

\(\displaystyle{\left|{{2}{x}+{4}}\right|}{>}{6}\)

\(2x+4<-6\)

\(2x<-6-4\)

\(2x<-10\)

\(x<-5\)

Or

\(2x+4>6\)

\(2x>6-4\)

\(2x>2\)

\(x>1\)

Step 4

So, final answer is:

\(x < -5\)

Or

\(x>1\)