Finite Math Examples

$\frac{m - 3}{15 m + 2} = \frac{3}{2}$

Step 1

Subtract $\frac{3}{2}$ from both sides of the equation.

$\frac{m - 3}{15 m + 2} - \frac{3}{2} = 0$

Step 2

Simplify $\frac{m - 3}{15 m + 2} - \frac{3}{2}$ .

Tap for more steps...

Step 2.1

To write $\frac{m - 3}{15 m + 2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{m - 3}{15 m + 2} \cdot \frac{2}{2} - \frac{3}{2} = 0$

Step 2.2

To write $- \frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{15 m + 2}{15 m + 2}$ .

$\frac{m - 3}{15 m + 2} \cdot \frac{2}{2} - \frac{3}{2} \cdot \frac{15 m + 2}{15 m + 2} = 0$

Step 2.3

Write each expression with a common denominator of $(15 m + 2) \cdot 2$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.3.1

Multiply $\frac{m - 3}{15 m + 2}$ by $\frac{2}{2}$ .

$\frac{(m - 3) \cdot 2}{(15 m + 2) \cdot 2} - \frac{3}{2} \cdot \frac{15 m + 2}{15 m + 2} = 0$

Step 2.3.2

Multiply $\frac{3}{2}$ by $\frac{15 m + 2}{15 m + 2}$ .

$\frac{(m - 3) \cdot 2}{(15 m + 2) \cdot 2} - \frac{3 (15 m + 2)}{2 (15 m + 2)} = 0$

Step 2.3.3

Reorder the factors of $(15 m + 2) \cdot 2$ .

$\frac{(m - 3) \cdot 2}{2 (15 m + 2)} - \frac{3 (15 m + 2)}{2 (15 m + 2)} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{(m - 3) \cdot 2 - 3 (15 m + 2)}{2 (15 m + 2)} = 0$

Step 2.5

Simplify the numerator.

Tap for more steps...

Step 2.5.1

Apply the distributive property.

$\frac{m \cdot 2 - 3 \cdot 2 - 3 (15 m + 2)}{2 (15 m + 2)} = 0$

Step 2.5.2

Move $2$ to the left of $m$ .

$\frac{2 \cdot m - 3 \cdot 2 - 3 (15 m + 2)}{2 (15 m + 2)} = 0$

Step 2.5.3

Multiply $- 3$ by $2$ .

$\frac{2 \cdot m - 6 - 3 (15 m + 2)}{2 (15 m + 2)} = 0$

Step 2.5.4

Apply the distributive property.

$\frac{2 m - 6 - 3 (15 m) - 3 \cdot 2}{2 (15 m + 2)} = 0$

Step 2.5.5

Multiply $15$ by $- 3$ .

$\frac{2 m - 6 - 45 m - 3 \cdot 2}{2 (15 m + 2)} = 0$

Step 2.5.6

Multiply $- 3$ by $2$ .

$\frac{2 m - 6 - 45 m - 6}{2 (15 m + 2)} = 0$

Step 2.5.7

Subtract $45 m$ from $2 m$ .

$\frac{- 43 m - 6 - 6}{2 (15 m + 2)} = 0$

Step 2.5.8

Subtract $6$ from $- 6$ .

$\frac{- 43 m - 12}{2 (15 m + 2)} = 0$

Step 2.6

Factor $- 1$ out of $- 43 m$ .

$\frac{- (43 m) - 12}{2 (15 m + 2)} = 0$

Step 2.7

Rewrite $- 12$ as $- 1 (12)$ .

$\frac{- (43 m) - 1 (12)}{2 (15 m + 2)} = 0$

Step 2.8

Factor $- 1$ out of $- (43 m) - 1 (12)$ .

$\frac{- (43 m + 12)}{2 (15 m + 2)} = 0$

Step 2.9

Rewrite $- (43 m + 12)$ as $- 1 (43 m + 12)$ .

$\frac{- 1 (43 m + 12)}{2 (15 m + 2)} = 0$

Step 2.10

Move the negative in front of the fraction.

$- \frac{43 m + 12}{2 (15 m + 2)} = 0$

Step 3

Set the numerator equal to zero.

$43 m + 12 = 0$

Step 4

Solve the equation for $m$ .

Tap for more steps...

Step 4.1

Subtract $12$ from both sides of the equation.

$43 m = - 12$

Step 4.2

Divide each term in $43 m = - 12$ by $43$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $43 m = - 12$ by $43$ .

$\frac{43 m}{43} = \frac{- 12}{43}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $43$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{43 m}{43} = \frac{- 12}{43}$

Step 4.2.2.1.2

Divide $m$ by $1$ .

$m = \frac{- 12}{43}$

Step 4.2.3

Simplify the right side.

Tap for more steps...

Step 4.2.3.1

Move the negative in front of the fraction.

$m = - \frac{12}{43}$