|2a-5|=9

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

2a-5=±9

Set up the positive portion of the ± solution.

2a-5=9

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

Add 5 to both sides of the equation.

2a=9+5

Add 9 and 5.

2a=14

2a=14

Divide each term by 2 and simplify.

Divide each term in 2a=14 by 2.

2a2=142

Cancel the common factor of 2.

Cancel the common factor.

2a2=142

Divide a by 1.

a=142

a=142

Divide 14 by 2.

a=7

a=7

a=7

Set up the negative portion of the ± solution.

2a-5=-9

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

Add 5 to both sides of the equation.

2a=-9+5

Add -9 and 5.

2a=-4

2a=-4

Divide each term by 2 and simplify.

Divide each term in 2a=-4 by 2.

2a2=-42

Cancel the common factor of 2.

Cancel the common factor.

2a2=-42

Divide a by 1.

a=-42

a=-42

Divide -4 by 2.

a=-2

a=-2

a=-2

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

a=7,-2

Solve for a |2a-5|=9