Question

Solve.
Absolute value of \(2x+4\) is greater than 6

Answer 1

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
\(x>1\)