Answer:-4<x<10
Step-by-step explanation:
STEP 1:
Rearrange this Absolute Value Inequality
Absolute value inequality entered
2|x-3|-4 < 10
Another term is moved/added to the right-hand side.
2|x-3| < 14
STEP 2:
Clear the Absolute Value Bars
Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.
The Absolute Value term is 2|x-3|
For the Negative case we'll use -2(x-3)
For the Positive case we'll use 2(x-3)
STEP 3:
Solve the Negative Case
-2(x-3) < 14
Multiply
-2x+6 < 14
Rearrange and Add up
-2x < 8
Divide both sides by 2
-x < 4
Multiply both sides by (-1)
Remember to flip the inequality sign
x > -4
Which is the solution for the Negative Case
STEP 4:
Solve the Positive Case
2(x-3) < 14
Multiply
2x-6 < 14
Rearrange and Add up
2x < 20
Divide both sides by 2
x < 10
Which is the solution for the Positive Case
STEP 5 :
Wrap up the solution
-4 < x < 10
