Basic Math Examples

$\frac{5 - 4 m}{3} = \frac{a - 7}{2}$

Step 1

Multiply both sides by $3$ .

$\frac{5 - 4 m}{3} \cdot 3 = \frac{a - 7}{2} \cdot 3$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{5 - 4 m}{3} \cdot 3$ .

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Step 2.1.1.1

Cancel the common factor of $3$ .

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Step 2.1.1.1.1

Cancel the common factor.

$\frac{5 - 4 m}{3} \cdot 3 = \frac{a - 7}{2} \cdot 3$

Step 2.1.1.1.2

Rewrite the expression.

$5 - 4 m = \frac{a - 7}{2} \cdot 3$

Step 2.1.1.2

Reorder $5$ and $- 4 m$ .

$- 4 m + 5 = \frac{a - 7}{2} \cdot 3$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{a - 7}{2} \cdot 3$ .

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Step 2.2.1.1

Combine $\frac{a - 7}{2}$ and $3$ .

$- 4 m + 5 = \frac{(a - 7) \cdot 3}{2}$

Step 2.2.1.2

Move $3$ to the left of $a - 7$ .

$- 4 m + 5 = \frac{3 (a - 7)}{2}$

Step 3

Solve for $m$ .

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Step 3.1

Subtract $5$ from both sides of the equation.

$- 4 m = \frac{3 (a - 7)}{2} - 5$

Step 3.2

Divide each term in $- 4 m = \frac{3 (a - 7)}{2} - 5$ by $- 4$ and simplify.

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Step 3.2.1

Divide each term in $- 4 m = \frac{3 (a - 7)}{2} - 5$ by $- 4$ .

$\frac{- 4 m}{- 4} = \frac{\frac{3 (a - 7)}{2}}{- 4} + \frac{- 5}{- 4}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 4$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 4 m}{- 4} = \frac{\frac{3 (a - 7)}{2}}{- 4} + \frac{- 5}{- 4}$

Step 3.2.2.1.2

Divide $m$ by $1$ .

$m = \frac{\frac{3 (a - 7)}{2}}{- 4} + \frac{- 5}{- 4}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Combine the numerators over the common denominator.

$m = \frac{\frac{3 (a - 7)}{2} - 5}{- 4}$

Step 3.2.3.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$m = \frac{\frac{3 (a - 7)}{2} - 5 \cdot \frac{2}{2}}{- 4}$

Step 3.2.3.3

Simplify terms.

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Step 3.2.3.3.1

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

$m = \frac{\frac{3 (a - 7)}{2} + \frac{- 5 \cdot 2}{2}}{- 4}$

Step 3.2.3.3.2

Combine the numerators over the common denominator.

$m = \frac{\frac{3 (a - 7) - 5 \cdot 2}{2}}{- 4}$

Step 3.2.3.4

Simplify the numerator.

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Step 3.2.3.4.1

Apply the distributive property.

$m = \frac{\frac{3 a + 3 \cdot - 7 - 5 \cdot 2}{2}}{- 4}$

Step 3.2.3.4.2

Multiply $3$ by $- 7$ .

$m = \frac{\frac{3 a - 21 - 5 \cdot 2}{2}}{- 4}$

Step 3.2.3.4.3

Multiply $- 5$ by $2$ .

$m = \frac{\frac{3 a - 21 - 10}{2}}{- 4}$

Step 3.2.3.4.4

Subtract $10$ from $- 21$ .

$m = \frac{\frac{3 a - 31}{2}}{- 4}$

Step 3.2.3.5

Multiply the numerator by the reciprocal of the denominator.

$m = \frac{3 a - 31}{2} \cdot \frac{1}{- 4}$

Step 3.2.3.6

Move the negative in front of the fraction.

$m = \frac{3 a - 31}{2} (- \frac{1}{4})$

Step 3.2.3.7

Multiply $\frac{3 a - 31}{2} (- \frac{1}{4})$ .

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Step 3.2.3.7.1

Multiply $\frac{3 a - 31}{2}$ by $\frac{1}{4}$ .

$m = - \frac{3 a - 31}{2 \cdot 4}$

Step 3.2.3.7.2

Multiply $2$ by $4$ .

$m = - \frac{3 a - 31}{8}$