|3x-2|+4=11

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

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

Add 2 to both sides of the equation.

3x=7+2

Add 7 and 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

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

Add 2 to both sides of the equation.

3x=-7+2

Add -7 and 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