|b+5|=2b-9

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

b+5=±(2b-9)

Set up the positive portion of the ± solution.

b+5=2b-9

Move all terms containing b to the left side of the equation.

Subtract 2b from both sides of the equation.

b+5-2b=-9

Subtract 2b from b.

-b+5=-9

-b+5=-9

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

Subtract 5 from both sides of the equation.

-b=-9-5

Subtract 5 from -9.

-b=-14

-b=-14

Multiply each term in -b=-14 by -1

Multiply each term in -b=-14 by -1.

(-b)⋅-1=(-14)⋅-1

Multiply (-b)⋅-1.

Multiply -1 by -1.

1b=(-14)⋅-1

Multiply b by 1.

b=(-14)⋅-1

b=(-14)⋅-1

Multiply -14 by -1.

b=14

b=14

b=14

Set up the negative portion of the ± solution.

b+5=-(2b-9)

Simplify -(2b-9).

Apply the distributive property.

b+5=-(2b)–9

Multiply.

Multiply 2 by -1.

b+5=-2b–9

Multiply -1 by -9.

b+5=-2b+9

b+5=-2b+9

b+5=-2b+9

Move all terms containing b to the left side of the equation.

Add 2b to both sides of the equation.

b+5+2b=9

Add b and 2b.

3b+5=9

3b+5=9

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

Subtract 5 from both sides of the equation.

3b=9-5

Subtract 5 from 9.

3b=4

3b=4

Divide each term by 3 and simplify.

Divide each term in 3b=4 by 3.

3b3=43

Cancel the common factor of 3.

Cancel the common factor.

3b3=43

Divide b by 1.

b=43

b=43

b=43

b=43

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

b=14,43

Exclude the solutions that do not make |b+5|=2b-9 true.

b=14

Solve for b |b+5|=2b-9