# Solve for b |4b+3|=13

|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
Solve the first equation for b.
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
Solve the second equation for b.
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

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