Finite Math Examples

$\frac{- 2 x}{3} + \frac{4 x}{5} = - 7$

Step 1

Simplify $\frac{- 2 x}{3} + \frac{4 x}{5}$ .

Tap for more steps...

Step 1.1

Move the negative in front of the fraction.

$- \frac{2 x}{3} + \frac{4 x}{5} = - 7$

Step 1.2

To write $- \frac{2 x}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 1.3

To write $\frac{4 x}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.4

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.4.1

Multiply $\frac{2 x}{3}$ by $\frac{5}{5}$ .

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

Step 1.4.2

Multiply $3$ by $5$ .

$- \frac{2 x \cdot 5}{15} + \frac{4 x}{5} \cdot \frac{3}{3} = - 7$

Step 1.4.3

Multiply $\frac{4 x}{5}$ by $\frac{3}{3}$ .

$- \frac{2 x \cdot 5}{15} + \frac{4 x \cdot 3}{5 \cdot 3} = - 7$

Step 1.4.4

Multiply $5$ by $3$ .

$- \frac{2 x \cdot 5}{15} + \frac{4 x \cdot 3}{15} = - 7$

Step 1.5

Combine the numerators over the common denominator.

$\frac{- 2 x \cdot 5 + 4 x \cdot 3}{15} = - 7$

Step 1.6

Simplify the numerator.

Tap for more steps...

Step 1.6.1

Factor $2 x$ out of $- 2 x \cdot 5 + 4 x \cdot 3$ .

Tap for more steps...

Step 1.6.1.1

Factor $2 x$ out of $- 2 x \cdot 5$ .

$\frac{2 x (- 1 \cdot 5) + 4 x \cdot 3}{15} = - 7$

Step 1.6.1.2

Factor $2 x$ out of $4 x \cdot 3$ .

$\frac{2 x (- 1 \cdot 5) + 2 x (2 \cdot 3)}{15} = - 7$

Step 1.6.1.3

Factor $2 x$ out of $2 x (- 1 \cdot 5) + 2 x (2 \cdot 3)$ .

$\frac{2 x (- 1 \cdot 5 + 2 \cdot 3)}{15} = - 7$

Step 1.6.2

Combine exponents.

Tap for more steps...

Step 1.6.2.1

Multiply $- 1$ by $5$ .

$\frac{2 x (- 5 + 2 \cdot 3)}{15} = - 7$

Step 1.6.2.2

Multiply $2$ by $3$ .

$\frac{2 x (- 5 + 6)}{15} = - 7$

Step 1.6.3

Add $- 5$ and $6$ .

$\frac{2 x \cdot 1}{15} = - 7$

Step 1.6.4

Multiply $2$ by $1$ .

$\frac{2 x}{15} = - 7$

Step 2

Multiply both sides of the equation by $\frac{15}{2}$ .

$\frac{15}{2} \cdot \frac{2 x}{15} = \frac{15}{2} \cdot - 7$

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 $\frac{15}{2} \cdot \frac{2 x}{15}$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor of $15$ .

Tap for more steps...

Step 3.1.1.1.1

Cancel the common factor.

$\frac{15}{2} \cdot \frac{2 x}{15} = \frac{15}{2} \cdot - 7$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{15}{2} \cdot - 7$

Step 3.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.1.2.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{15}{2} \cdot - 7$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{15}{2} \cdot - 7$

Step 3.1.1.2.3

Rewrite the expression.

$x = \frac{15}{2} \cdot - 7$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Simplify $\frac{15}{2} \cdot - 7$ .

Tap for more steps...

Step 3.2.1.1

Multiply $\frac{15}{2} \cdot - 7$ .

Tap for more steps...

Step 3.2.1.1.1

Combine $\frac{15}{2}$ and $- 7$ .

$x = \frac{15 \cdot - 7}{2}$

Step 3.2.1.1.2

Multiply $15$ by $- 7$ .

$x = \frac{- 105}{2}$

Step 3.2.1.2

Move the negative in front of the fraction.

$x = - \frac{105}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{105}{2}$

Decimal Form:

$x = - 52.5$

Mixed Number Form:

$x = - 52 \frac{1}{2}$