Solve for b -14=2/5*(9-2b)

$- 14 = \frac{2}{5} \cdot (9 - 2 b)$

Step 1

Rewrite the equation as $\frac{2}{5} \cdot (9 - 2 b) = - 14$ .

$\frac{2}{5} \cdot (9 - 2 b) = - 14$

Step 2

Multiply both sides of the equation by $\frac{5}{2}$ .

$\frac{5}{2} (\frac{2}{5} \cdot (9 - 2 b)) = \frac{5}{2} \cdot - 14$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{5}{2} (\frac{2}{5} \cdot (9 - 2 b))$ .

Apply the distributive property.

$\frac{5}{2} (\frac{2}{5} \cdot 9 + \frac{2}{5} (- 2 b)) = \frac{5}{2} \cdot - 14$

Multiply $\frac{2}{5} \cdot 9$ .

Combine $\frac{2}{5}$ and $9$ .

$\frac{5}{2} (\frac{2 \cdot 9}{5} + \frac{2}{5} (- 2 b)) = \frac{5}{2} \cdot - 14$

Multiply $2$ by $9$ .

$\frac{5}{2} (\frac{18}{5} + \frac{2}{5} (- 2 b)) = \frac{5}{2} \cdot - 14$

Multiply $\frac{2}{5} (- 2 b)$ .

Combine $- 2$ and $\frac{2}{5}$ .

$\frac{5}{2} (\frac{18}{5} + \frac{- 2 \cdot 2}{5} b) = \frac{5}{2} \cdot - 14$

Multiply $- 2$ by $2$ .

$\frac{5}{2} (\frac{18}{5} + \frac{- 4}{5} b) = \frac{5}{2} \cdot - 14$

Combine $\frac{- 4}{5}$ and $b$ .

$\frac{5}{2} (\frac{18}{5} + \frac{- 4 b}{5}) = \frac{5}{2} \cdot - 14$

Move the negative in front of the fraction.

$\frac{5}{2} (\frac{18}{5} - \frac{4 b}{5}) = \frac{5}{2} \cdot - 14$

Simplify terms.

Apply the distributive property.

$\frac{5}{2} \cdot \frac{18}{5} + \frac{5}{2} (- \frac{4 b}{5}) = \frac{5}{2} \cdot - 14$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5}{2} \cdot \frac{18}{5} + \frac{5}{2} (- \frac{4 b}{5}) = \frac{5}{2} \cdot - 14$

Rewrite the expression.

$\frac{1}{2} \cdot 18 + \frac{5}{2} (- \frac{4 b}{5}) = \frac{5}{2} \cdot - 14$

Cancel the common factor of $2$ .

Factor $2$ out of $18$ .

$\frac{1}{2} \cdot (2 (9)) + \frac{5}{2} (- \frac{4 b}{5}) = \frac{5}{2} \cdot - 14$

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 9) + \frac{5}{2} (- \frac{4 b}{5}) = \frac{5}{2} \cdot - 14$

Rewrite the expression.

$9 + \frac{5}{2} (- \frac{4 b}{5}) = \frac{5}{2} \cdot - 14$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{4 b}{5}$ into the numerator.

$9 + \frac{5}{2} \cdot \frac{- 4 b}{5} = \frac{5}{2} \cdot - 14$

Cancel the common factor.

$9 + \frac{5}{2} \cdot \frac{- 4 b}{5} = \frac{5}{2} \cdot - 14$

Rewrite the expression.

$9 + \frac{1}{2} (- 4 b) = \frac{5}{2} \cdot - 14$

Cancel the common factor of $2$ .

Factor $2$ out of $- 4 b$ .

$9 + \frac{1}{2} (2 (- 2 b)) = \frac{5}{2} \cdot - 14$

Cancel the common factor.

$9 + \frac{1}{2} (2 (- 2 b)) = \frac{5}{2} \cdot - 14$

Rewrite the expression.

$9 - 2 b = \frac{5}{2} \cdot - 14$

Simplify the right side.

Simplify $\frac{5}{2} \cdot - 14$ .

Cancel the common factor of $2$ .

Factor $2$ out of $- 14$ .

$9 - 2 b = \frac{5}{2} \cdot (2 (- 7))$

Cancel the common factor.

$9 - 2 b = \frac{5}{2} \cdot (2 \cdot - 7)$

Rewrite the expression.

$9 - 2 b = 5 \cdot - 7$

Multiply $5$ by $- 7$ .

$9 - 2 b = - 35$

Step 4

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

Subtract $9$ from both sides of the equation.

$- 2 b = - 35 - 9$

Subtract $9$ from $- 35$ .

$- 2 b = - 44$

Step 5

Divide each term in $- 2 b = - 44$ by $- 2$ and simplify.

Divide each term in $- 2 b = - 44$ by $- 2$ .

$\frac{- 2 b}{- 2} = \frac{- 44}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 b}{- 2} = \frac{- 44}{- 2}$

Divide $b$ by $1$ .

$b = \frac{- 44}{- 2}$

Simplify the right side.

Divide $- 44$ by $- 2$ .

$b = 22$

Solve for b -14=2/5*(9-2b)

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