Basic Math Examples

$\frac{5}{7} m - 2 - \frac{6}{7} m = - 13$

Step 1

Simplify $\frac{5}{7} m - 2 - \frac{6}{7} m$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{5}{7}$ and $m$ .

$\frac{5 m}{7} - 2 - \frac{6}{7} m = - 13$

Step 1.1.2

Combine $m$ and $\frac{6}{7}$ .

$\frac{5 m}{7} - 2 - \frac{m \cdot 6}{7} = - 13$

Step 1.1.3

Move $6$ to the left of $m$ .

$\frac{5 m}{7} - 2 - \frac{6 m}{7} = - 13$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the numerators over the common denominator.

$- 2 + \frac{5 m - 6 m}{7} = - 13$

Step 1.2.2

Subtract $6 m$ from $5 m$ .

$- 2 + \frac{- m}{7} = - 13$

Step 1.2.3

Move the negative in front of the fraction.

$- 2 - \frac{m}{7} = - 13$

Step 2

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

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Step 2.1

Add $2$ to both sides of the equation.

$- \frac{m}{7} = - 13 + 2$

Step 2.2

Add $- 13$ and $2$ .

$- \frac{m}{7} = - 11$

Step 3

Multiply both sides of the equation by $- 7$ .

$- 7 (- \frac{m}{7}) = - 7 \cdot - 11$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $- 7 (- \frac{m}{7})$ .

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Step 4.1.1.1

Cancel the common factor of $7$ .

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Step 4.1.1.1.1

Move the leading negative in $- \frac{m}{7}$ into the numerator.

$- 7 \frac{- m}{7} = - 7 \cdot - 11$

Step 4.1.1.1.2

Factor $7$ out of $- 7$ .

$7 (- 1) \frac{- m}{7} = - 7 \cdot - 11$

Step 4.1.1.1.3

Cancel the common factor.

$7 \cdot - 1 \frac{- m}{7} = - 7 \cdot - 11$

Step 4.1.1.1.4

Rewrite the expression.

$- - m = - 7 \cdot - 11$

Step 4.1.1.2

Multiply.

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Step 4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 m = - 7 \cdot - 11$

Step 4.1.1.2.2

Multiply $m$ by $1$ .

$m = - 7 \cdot - 11$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 7$ by $- 11$ .

$m = 77$