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.

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

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