Basic Math Examples

$\frac{m - 15}{5} - \frac{7 m - 7}{6} = 3$

Step 1

Simplify $\frac{m - 15}{5} - \frac{7 m - 7}{6}$ .

Tap for more steps...

Step 1.1

Factor $7$ out of $7 m - 7$ .

Tap for more steps...

Step 1.1.1

Factor $7$ out of $7 m$ .

$\frac{m - 15}{5} - \frac{7 (m) - 7}{6} = 3$

Step 1.1.2

Factor $7$ out of $- 7$ .

$\frac{m - 15}{5} - \frac{7 (m) + 7 (- 1)}{6} = 3$

Step 1.1.3

Factor $7$ out of $7 (m) + 7 (- 1)$ .

$\frac{m - 15}{5} - \frac{7 (m - 1)}{6} = 3$

Step 1.2

To write $\frac{m - 15}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{m - 15}{5} \cdot \frac{6}{6} - \frac{7 (m - 1)}{6} = 3$

Step 1.3

To write $- \frac{7 (m - 1)}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{m - 15}{5} \cdot \frac{6}{6} - \frac{7 (m - 1)}{6} \cdot \frac{5}{5} = 3$

Step 1.4

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.4.1

Multiply $\frac{m - 15}{5}$ by $\frac{6}{6}$ .

$\frac{(m - 15) \cdot 6}{5 \cdot 6} - \frac{7 (m - 1)}{6} \cdot \frac{5}{5} = 3$

Step 1.4.2

Multiply $5$ by $6$ .

$\frac{(m - 15) \cdot 6}{30} - \frac{7 (m - 1)}{6} \cdot \frac{5}{5} = 3$

Step 1.4.3

Multiply $\frac{7 (m - 1)}{6}$ by $\frac{5}{5}$ .

$\frac{(m - 15) \cdot 6}{30} - \frac{7 (m - 1) \cdot 5}{6 \cdot 5} = 3$

Step 1.4.4

Multiply $6$ by $5$ .

$\frac{(m - 15) \cdot 6}{30} - \frac{7 (m - 1) \cdot 5}{30} = 3$

Step 1.5

Combine the numerators over the common denominator.

$\frac{(m - 15) \cdot 6 - 7 (m - 1) \cdot 5}{30} = 3$

Step 1.6

Simplify the numerator.

Tap for more steps...

Step 1.6.1

Apply the distributive property.

$\frac{m \cdot 6 - 15 \cdot 6 - 7 (m - 1) \cdot 5}{30} = 3$

Step 1.6.2

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

$\frac{6 \cdot m - 15 \cdot 6 - 7 (m - 1) \cdot 5}{30} = 3$

Step 1.6.3

Multiply $- 15$ by $6$ .

$\frac{6 \cdot m - 90 - 7 (m - 1) \cdot 5}{30} = 3$

Step 1.6.4

Apply the distributive property.

$\frac{6 m - 90 + (- 7 m - 7 \cdot - 1) \cdot 5}{30} = 3$

Step 1.6.5

Multiply $- 7$ by $- 1$ .

$\frac{6 m - 90 + (- 7 m + 7) \cdot 5}{30} = 3$

Step 1.6.6

Apply the distributive property.

$\frac{6 m - 90 - 7 m \cdot 5 + 7 \cdot 5}{30} = 3$

Step 1.6.7

Multiply $5$ by $- 7$ .

$\frac{6 m - 90 - 35 m + 7 \cdot 5}{30} = 3$

Step 1.6.8

Multiply $7$ by $5$ .

$\frac{6 m - 90 - 35 m + 35}{30} = 3$

Step 1.6.9

Subtract $35 m$ from $6 m$ .

$\frac{- 29 m - 90 + 35}{30} = 3$

Step 1.6.10

Add $- 90$ and $35$ .

$\frac{- 29 m - 55}{30} = 3$

Step 1.7

Simplify with factoring out.

Tap for more steps...

Step 1.7.1

Factor $- 1$ out of $- 29 m$ .

$\frac{- (29 m) - 55}{30} = 3$

Step 1.7.2

Rewrite $- 55$ as $- 1 (55)$ .

$\frac{- (29 m) - 1 (55)}{30} = 3$

Step 1.7.3

Factor $- 1$ out of $- (29 m) - 1 (55)$ .

$\frac{- (29 m + 55)}{30} = 3$

Step 1.7.4

Simplify the expression.

Tap for more steps...

Step 1.7.4.1

Rewrite $- (29 m + 55)$ as $- 1 (29 m + 55)$ .

$\frac{- 1 (29 m + 55)}{30} = 3$

Step 1.7.4.2

Move the negative in front of the fraction.

$- \frac{29 m + 55}{30} = 3$

Step 2

Multiply both sides of the equation by $- 30$ .

$- 30 (- \frac{29 m + 55}{30}) = - 30 \cdot 3$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $- 30 (- \frac{29 m + 55}{30})$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor of $30$ .

Tap for more steps...

Step 3.1.1.1.1

Move the leading negative in $- \frac{29 m + 55}{30}$ into the numerator.

$- 30 \frac{- (29 m + 55)}{30} = - 30 \cdot 3$

Step 3.1.1.1.2

Factor $30$ out of $- 30$ .

$30 (- 1) \frac{- (29 m + 55)}{30} = - 30 \cdot 3$

Step 3.1.1.1.3

Cancel the common factor.

$30 \cdot - 1 \frac{- (29 m + 55)}{30} = - 30 \cdot 3$

Step 3.1.1.1.4

Rewrite the expression.

$- - (29 m + 55) = - 30 \cdot 3$

Step 3.1.1.2

Multiply.

Tap for more steps...

Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (29 m + 55) = - 30 \cdot 3$

Step 3.1.1.2.2

Multiply $29 m + 55$ by $1$ .

$29 m + 55 = - 30 \cdot 3$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $- 30$ by $3$ .

$29 m + 55 = - 90$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $55$ from both sides of the equation.

$29 m = - 90 - 55$

Step 4.2

Subtract $55$ from $- 90$ .

$29 m = - 145$

Step 5

Divide each term in $29 m = - 145$ by $29$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $29 m = - 145$ by $29$ .

$\frac{29 m}{29} = \frac{- 145}{29}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $29$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{29 m}{29} = \frac{- 145}{29}$

Step 5.2.1.2

Divide $m$ by $1$ .

$m = \frac{- 145}{29}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Divide $- 145$ by $29$ .

$m = - 5$