Basic Math Examples

$- 17 = - 32 - \frac{3}{5} f$

Step 1

Rewrite the equation as $- 32 - \frac{3}{5} f = - 17$ .

$- 32 - \frac{3}{5} f = - 17$

Step 2

Simplify each term.

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Step 2.1

Combine $f$ and $\frac{3}{5}$ .

$- 32 - \frac{f \cdot 3}{5} = - 17$

Step 2.2

Move $3$ to the left of $f$ .

$- 32 - \frac{3 f}{5} = - 17$

Step 3

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

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Step 3.1

Add $32$ to both sides of the equation.

$- \frac{3 f}{5} = - 17 + 32$

Step 3.2

Add $- 17$ and $32$ .

$- \frac{3 f}{5} = 15$

Step 4

Multiply both sides of the equation by $- \frac{5}{3}$ .

$- \frac{5}{3} (- \frac{3 f}{5}) = - \frac{5}{3} \cdot 15$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- \frac{5}{3} (- \frac{3 f}{5})$ .

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Step 5.1.1.1

Cancel the common factor of $5$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{5}{3}$ into the numerator.

$\frac{- 5}{3} (- \frac{3 f}{5}) = - \frac{5}{3} \cdot 15$

Step 5.1.1.1.2

Move the leading negative in $- \frac{3 f}{5}$ into the numerator.

$\frac{- 5}{3} \cdot \frac{- 3 f}{5} = - \frac{5}{3} \cdot 15$

Step 5.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{3} \cdot \frac{- 3 f}{5} = - \frac{5}{3} \cdot 15$

Step 5.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{3} \cdot \frac{- 3 f}{5} = - \frac{5}{3} \cdot 15$

Step 5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{3} (- 3 f) = - \frac{5}{3} \cdot 15$

Step 5.1.1.2

Cancel the common factor of $3$ .

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Step 5.1.1.2.1

Factor $3$ out of $- 3 f$ .

$\frac{- 1}{3} (3 (- f)) = - \frac{5}{3} \cdot 15$

Step 5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{3} (3 (- f)) = - \frac{5}{3} \cdot 15$

Step 5.1.1.2.3

Rewrite the expression.

$- - f = - \frac{5}{3} \cdot 15$

Step 5.1.1.3

Multiply.

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Step 5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 f = - \frac{5}{3} \cdot 15$

Step 5.1.1.3.2

Multiply $f$ by $1$ .

$f = - \frac{5}{3} \cdot 15$

Step 5.2

Simplify the right side.

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Step 5.2.1

Simplify $- \frac{5}{3} \cdot 15$ .

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Step 5.2.1.1

Cancel the common factor of $3$ .

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Step 5.2.1.1.1

Move the leading negative in $- \frac{5}{3}$ into the numerator.

$f = \frac{- 5}{3} \cdot 15$

Step 5.2.1.1.2

Factor $3$ out of $15$ .

$f = \frac{- 5}{3} \cdot (3 (5))$

Step 5.2.1.1.3

Cancel the common factor.

$f = \frac{- 5}{3} \cdot (3 \cdot 5)$

Step 5.2.1.1.4

Rewrite the expression.

$f = - 5 \cdot 5$

Step 5.2.1.2

Multiply $- 5$ by $5$ .

$f = - 25$