Basic Math Examples

$| b + 5 | = 2 b - 9$

Step 1

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

$b + 5 = \pm (2 b - 9)$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.1

First, use the positive value of the $\pm$ to find the first solution.

$b + 5 = 2 b - 9$

Step 2.2

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

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Step 2.2.1

Subtract $2 b$ from both sides of the equation.

$b + 5 - 2 b = - 9$

Step 2.2.2

Subtract $2 b$ from $b$ .

$- b + 5 = - 9$

Step 2.3

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

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Step 2.3.1

Subtract $5$ from both sides of the equation.

$- b = - 9 - 5$

Step 2.3.2

Subtract $5$ from $- 9$ .

$- b = - 14$

Step 2.4

Divide each term in $- b = - 14$ by $- 1$ and simplify.

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Step 2.4.1

Divide each term in $- b = - 14$ by $- 1$ .

$\frac{- b}{- 1} = \frac{- 14}{- 1}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Dividing two negative values results in a positive value.

$\frac{b}{1} = \frac{- 14}{- 1}$

Step 2.4.2.2

Divide $b$ by $1$ .

$b = \frac{- 14}{- 1}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Divide $- 14$ by $- 1$ .

$b = 14$

Step 2.5

Next, use the negative value of the $\pm$ to find the second solution.

$b + 5 = - (2 b - 9)$

Step 2.6

Simplify $- (2 b - 9)$ .

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Step 2.6.1

Rewrite.

$b + 5 = 0 + 0 - (2 b - 9)$

Step 2.6.2

Simplify by adding zeros.

$b + 5 = - (2 b - 9)$

Step 2.6.3

Apply the distributive property.

$b + 5 = - (2 b) - - 9$

Step 2.6.4

Multiply.

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Step 2.6.4.1

Multiply $2$ by $- 1$ .

$b + 5 = - 2 b - - 9$

Step 2.6.4.2

Multiply $- 1$ by $- 9$ .

$b + 5 = - 2 b + 9$

Step 2.7

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

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Step 2.7.1

Add $2 b$ to both sides of the equation.

$b + 5 + 2 b = 9$

Step 2.7.2

Add $b$ and $2 b$ .

$3 b + 5 = 9$

Step 2.8

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

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Step 2.8.1

Subtract $5$ from both sides of the equation.

$3 b = 9 - 5$

Step 2.8.2

Subtract $5$ from $9$ .

$3 b = 4$

Step 2.9

Divide each term in $3 b = 4$ by $3$ and simplify.

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Step 2.9.1

Divide each term in $3 b = 4$ by $3$ .

$\frac{3 b}{3} = \frac{4}{3}$

Step 2.9.2

Simplify the left side.

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Step 2.9.2.1

Cancel the common factor of $3$ .

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Step 2.9.2.1.1

Cancel the common factor.

$\frac{3 b}{3} = \frac{4}{3}$

Step 2.9.2.1.2

Divide $b$ by $1$ .

$b = \frac{4}{3}$

Step 2.10

The complete solution is the result of both the positive and negative portions of the solution.

$b = 14, \frac{4}{3}$

Step 3

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

$b = 14$