Question

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

Piecewise-Defined Functions

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

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
$$\displaystyle{\left|{{2}{x}+{4}}\right|}{>}{6}$$
$$2x+4<-6$$
$$2x<-6-4$$
$$2x<-10$$
$$x<-5$$
Or
$$2x+4>6$$
$$2x>6-4$$
$$2x>2$$
$$x>1$$
Step 4
$$x < -5$$
$$x>1$$