# Solve for a |5a+3|=5

|5a+3|=5
Remove the absolute value term. This creates a ± on the right side of the equation because |x|=±x.
5a+3=±5
Set up the positive portion of the ± solution.
5a+3=5
Solve the first equation for a.
Move all terms not containing a to the right side of the equation.
Subtract 3 from both sides of the equation.
5a=5-3
Subtract 3 from 5.
5a=2
5a=2
Divide each term by 5 and simplify.
Divide each term in 5a=2 by 5.
5a5=25
Cancel the common factor of 5.
Cancel the common factor.
5a5=25
Divide a by 1.
a=25
a=25
a=25
a=25
Set up the negative portion of the ± solution.
5a+3=-5
Solve the second equation for a.
Move all terms not containing a to the right side of the equation.
Subtract 3 from both sides of the equation.
5a=-5-3
Subtract 3 from -5.
5a=-8
5a=-8
Divide each term by 5 and simplify.
Divide each term in 5a=-8 by 5.
5a5=-85
Cancel the common factor of 5.
Cancel the common factor.
5a5=-85
Divide a by 1.
a=-85
a=-85
Move the negative in front of the fraction.
a=-85
a=-85
a=-85
The solution to the equation includes both the positive and negative portions of the solution.
a=25,-85
The result can be shown in multiple forms.
Exact Form:
a=25,-85
Decimal Form:
a=0.4,-1.6
Mixed Number Form:
a=25,-135
Solve for a |5a+3|=5

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