Answer:
x>1 negative
x<(-1/2) positive
Step-by-step explanation:
Rearrange this Absolute Value Inequality
Absolute value inequalitiy entered
|-4x+1| > 3
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 |-4x+1|
For the Negative case we'll use -(-4x+1)
Solve the Negative Case
-(-4x+1) > 3
Multiply
4x-1 > 3
Rearrange and Add up
4x > 4
Divide both sides by 4
x > 1 for the negative
For the Positive case we'll use (-4x+1)
(-4x+1) > 3
Rearrange and Add up
-4x > 2
Divide both sides by 4
-x > (1/2)
Multiply both sides by (-1)
Remember to flip the inequality sign
x < -(1/2)
Which is the solution for the Positive Case
Answer for Q.2:
x=-2/5 negative
x=-2 poisitive
Explanation:
Rearrange this Absolute Value Equation
Absolute value equalitiy entered
|x-2| = 4x+4
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 |x-2|
For the Negative case we'll use -(x-2)
For the Positive case we'll use (x-2)
STEP
3
:
Solve the Negative Case
-(x-2) = 4x+4
Multiply
-x+2 = 4x+4
Rearrange and Add up
-5x = 2
Divide both sides by 5
-x = (2/5)
Multiply both sides by (-1)
x = -(2/5)
Which is the solution for the Negative Case
(x-2) = 4x+4
Rearrange and Add up
-3x = 6
Divide both sides by 3
-x = 2
Multiply both sides by (-1)
x = -2
Which is the solution for the Positive Case
