|4b+3|=13

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

4b+3=±13

Set up the positive portion of the ± solution.

4b+3=13

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

Subtract 3 from both sides of the equation.

4b=13-3

Subtract 3 from 13.

4b=10

4b=10

Divide each term by 4 and simplify.

Divide each term in 4b=10 by 4.

4b4=104

Cancel the common factor of 4.

Cancel the common factor.

4b4=104

Divide b by 1.

b=104

b=104

Cancel the common factor of 10 and 4.

Factor 2 out of 10.

b=2(5)4

Cancel the common factors.

Factor 2 out of 4.

b=2⋅52⋅2

Cancel the common factor.

b=2⋅52⋅2

Rewrite the expression.

b=52

b=52

b=52

b=52

b=52

Set up the negative portion of the ± solution.

4b+3=-13

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

Subtract 3 from both sides of the equation.

4b=-13-3

Subtract 3 from -13.

4b=-16

4b=-16

Divide each term by 4 and simplify.

Divide each term in 4b=-16 by 4.

4b4=-164

Cancel the common factor of 4.

Cancel the common factor.

4b4=-164

Divide b by 1.

b=-164

b=-164

Divide -16 by 4.

b=-4

b=-4

b=-4

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

b=52,-4

The result can be shown in multiple forms.

Exact Form:

b=52,-4

Decimal Form:

b=2.5,-4

Mixed Number Form:

b=212,-4

Solve for b |4b+3|=13