Basic Math Examples

- \frac{7}{5} a = 28

$- \frac{7}{5} a = 28$

Step 1

Multiply both sides of the equation by

- \frac{5}{7}

$- \frac{5}{7}$ .

- \frac{5}{7} (- \frac{7}{5} a) = - \frac{5}{7} \cdot 28

$- \frac{5}{7} (- \frac{7}{5} a) = - \frac{5}{7} \cdot 28$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify

- \frac{5}{7} (- \frac{7}{5} a)

$- \frac{5}{7} (- \frac{7}{5} a)$ .

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Step 2.1.1.1

Combine

a

$a$ and

\frac{7}{5}

$\frac{7}{5}$ .

- \frac{5}{7} (- \frac{a \cdot 7}{5}) = - \frac{5}{7} \cdot 28

$- \frac{5}{7} (- \frac{a \cdot 7}{5}) = - \frac{5}{7} \cdot 28$

Step 2.1.1.2

Cancel the common factor of

5

$5$ .

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Step 2.1.1.2.1

Move the leading negative in

- \frac{5}{7}

$- \frac{5}{7}$ into the numerator.

\frac{- 5}{7} (- \frac{a \cdot 7}{5}) = - \frac{5}{7} \cdot 28

$\frac{- 5}{7} (- \frac{a \cdot 7}{5}) = - \frac{5}{7} \cdot 28$

Step 2.1.1.2.2

Move the leading negative in

- \frac{a \cdot 7}{5}

$- \frac{a \cdot 7}{5}$ into the numerator.

\frac{- 5}{7} \cdot \frac{- a \cdot 7}{5} = - \frac{5}{7} \cdot 28

$\frac{- 5}{7} \cdot \frac{- a \cdot 7}{5} = - \frac{5}{7} \cdot 28$

Step 2.1.1.2.3

Factor

$5$ out of

$- 5$ .

$\frac{5 (- 1)}{7} \cdot \frac{- a \cdot 7}{5} = - \frac{5}{7} \cdot 28$

Step 2.1.1.2.4

Cancel the common factor.

$\frac{5 \cdot - 1}{7} \cdot \frac{- a \cdot 7}{5} = - \frac{5}{7} \cdot 28$

Step 2.1.1.2.5

Rewrite the expression.

$\frac{- 1}{7} (- a \cdot 7) = - \frac{5}{7} \cdot 28$

Step 2.1.1.3

Cancel the common factor of

$7$ .

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Step 2.1.1.3.1

Factor

$7$ out of

$- a \cdot 7$ .

$\frac{- 1}{7} (7 \cdot (- a)) = - \frac{5}{7} \cdot 28$

Step 2.1.1.3.2

Cancel the common factor.

$\frac{- 1}{7} (7 \cdot (- a)) = - \frac{5}{7} \cdot 28$

Step 2.1.1.3.3

Rewrite the expression.

$- - a = - \frac{5}{7} \cdot 28$

Step 2.1.1.4

Multiply.

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Step 2.1.1.4.1

Multiply

$- 1$ by

$- 1$ .

$1 a = - \frac{5}{7} \cdot 28$

Step 2.1.1.4.2

Multiply

$a$ by

$1$ .

$a = - \frac{5}{7} \cdot 28$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify

$- \frac{5}{7} \cdot 28$ .

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Step 2.2.1.1

Cancel the common factor of

$7$ .

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Step 2.2.1.1.1

Move the leading negative in

$- \frac{5}{7}$ into the numerator.

$a = \frac{- 5}{7} \cdot 28$

Step 2.2.1.1.2

Factor

$7$ out of

$28$ .

$a = \frac{- 5}{7} \cdot (7 (4))$

Step 2.2.1.1.3

Cancel the common factor.

$a = \frac{- 5}{7} \cdot (7 \cdot 4)$

Step 2.2.1.1.4

Rewrite the expression.

$a = - 5 \cdot 4$

Step 2.2.1.2

Multiply

$- 5$ by

$4$ .

$a = - 20$