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

Question
Piecewise-Defined Functions
asked 2021-03-06
Solve.
Absolute value of 2x+4 is greater than 6

Answers (1)

2021-03-07
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
2x
2x
x
Or
2x+4>6
2x>6-4
2x>2
x>1
Step 4
So, final answer is:
x < -5
Or
x>1
0

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