# Solve for x |3x-2|+4=11

|3x-2|+4=11
Move all terms not containing |3x-2| to the right side of the equation.
Subtract 4 from both sides of the equation.
|3x-2|=11-4
Subtract 4 from 11.
|3x-2|=7
|3x-2|=7
Remove the absolute value term. This creates a ± on the right side of the equation because |x|=±x.
3x-2=±7
Set up the positive portion of the ± solution.
3x-2=7
Solve the first equation for x.
Move all terms not containing x to the right side of the equation.
Add 2 to both sides of the equation.
3x=7+2
3x=9
3x=9
Divide each term by 3 and simplify.
Divide each term in 3x=9 by 3.
3×3=93
Cancel the common factor of 3.
Cancel the common factor.
3×3=93
Divide x by 1.
x=93
x=93
Divide 9 by 3.
x=3
x=3
x=3
Set up the negative portion of the ± solution.
3x-2=-7
Solve the second equation for x.
Move all terms not containing x to the right side of the equation.
Add 2 to both sides of the equation.
3x=-7+2
3x=-5
3x=-5
Divide each term by 3 and simplify.
Divide each term in 3x=-5 by 3.
3×3=-53
Cancel the common factor of 3.
Cancel the common factor.
3×3=-53
Divide x by 1.
x=-53
x=-53
Move the negative in front of the fraction.
x=-53
x=-53
x=-53
The solution to the equation includes both the positive and negative portions of the solution.
x=3,-53
The result can be shown in multiple forms.
Exact Form:
x=3,-53
Decimal Form:
x=3,-1.6‾
Mixed Number Form:
x=3,-123
Solve for x |3x-2|+4=11