Question

Can someone show and explain the steps to these problems?

1. a Classmate wrote the solution to the inequality |-4x+1|>3.

2. a classmate wrote the evolution to the equation |x-2|=4x+4.

Answer 1

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

Step-by-step 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