# Solve for b |b+5|=2b-9 |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
Solve the first equation for b.
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)
Solve the second equation for b.
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

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