|-4x+8|=1

Remove the absolute value term. This creates a ± on the right side of the equation because |x|=±x.

-4x+8=±1

Set up the positive portion of the ± solution.

-4x+8=1

Move all terms not containing x to the right side of the equation.

Subtract 8 from both sides of the equation.

-4x=1-8

Subtract 8 from 1.

-4x=-7

-4x=-7

Divide each term by -4 and simplify.

Divide each term in -4x=-7 by -4.

-4x-4=-7-4

Cancel the common factor of -4.

Cancel the common factor.

-4x-4=-7-4

Divide x by 1.

x=-7-4

x=-7-4

Dividing two negative values results in a positive value.

x=74

x=74

x=74

Set up the negative portion of the ± solution.

-4x+8=-1

Move all terms not containing x to the right side of the equation.

Subtract 8 from both sides of the equation.

-4x=-1-8

Subtract 8 from -1.

-4x=-9

-4x=-9

Divide each term by -4 and simplify.

Divide each term in -4x=-9 by -4.

-4x-4=-9-4

Cancel the common factor of -4.

Cancel the common factor.

-4x-4=-9-4

Divide x by 1.

x=-9-4

x=-9-4

Dividing two negative values results in a positive value.

x=94

x=94

x=94

The solution to the equation includes both the positive and negative portions of the solution.

x=74,94

The result can be shown in multiple forms.

Exact Form:

x=74,94

Decimal Form:

x=1.75,2.25

Mixed Number Form:

x=134,214

Solve for x |-4x+8|=1