# Solve for x |-4x+8|=1 |-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
Solve the first equation for x.
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
Solve the second equation for x.
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
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