Finite Math Examples

$\frac{8 x}{15} + \frac{3}{5} = \frac{x + 1}{2}$

Step 1

Multiply both sides by $2$ .

$(\frac{8 x}{15} + \frac{3}{5}) \cdot 2 = \frac{x + 1}{2} \cdot 2$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{8 x}{15} + \frac{3}{5}) \cdot 2$ .

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Step 2.1.1.1

Apply the distributive property.

$\frac{8 x}{15} \cdot 2 + \frac{3}{5} \cdot 2 = \frac{x + 1}{2} \cdot 2$

Step 2.1.1.2

Multiply $\frac{8 x}{15} \cdot 2$ .

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Step 2.1.1.2.1

Combine $\frac{8 x}{15}$ and $2$ .

$\frac{8 x \cdot 2}{15} + \frac{3}{5} \cdot 2 = \frac{x + 1}{2} \cdot 2$

Step 2.1.1.2.2

Multiply $2$ by $8$ .

$\frac{16 x}{15} + \frac{3}{5} \cdot 2 = \frac{x + 1}{2} \cdot 2$

Step 2.1.1.3

Multiply $\frac{3}{5} \cdot 2$ .

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Step 2.1.1.3.1

Combine $\frac{3}{5}$ and $2$ .

$\frac{16 x}{15} + \frac{3 \cdot 2}{5} = \frac{x + 1}{2} \cdot 2$

Step 2.1.1.3.2

Multiply $3$ by $2$ .

$\frac{16 x}{15} + \frac{6}{5} = \frac{x + 1}{2} \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{16 x}{15} + \frac{6}{5} = \frac{x + 1}{2} \cdot 2$

Step 2.2.1.2

Rewrite the expression.

$\frac{16 x}{15} + \frac{6}{5} = x + 1$

Step 3

Solve for $x$ .

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Subtract $x$ from both sides of the equation.

$\frac{16 x}{15} + \frac{6}{5} - x = 1$

Step 3.1.2

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

$\frac{16 x}{15} - x \cdot \frac{15}{15} + \frac{6}{5} = 1$

Step 3.1.3

Combine $- x$ and $\frac{15}{15}$ .

$\frac{16 x}{15} + \frac{- x \cdot 15}{15} + \frac{6}{5} = 1$

Step 3.1.4

Combine the numerators over the common denominator.

$\frac{16 x - x \cdot 15}{15} + \frac{6}{5} = 1$

Step 3.1.5

Simplify each term.

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Step 3.1.5.1

Simplify the numerator.

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Step 3.1.5.1.1

Factor $x$ out of $16 x - x \cdot 15$ .

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Step 3.1.5.1.1.1

Factor $x$ out of $16 x$ .

$\frac{x \cdot 16 - x \cdot 15}{15} + \frac{6}{5} = 1$

Step 3.1.5.1.1.2

Factor $x$ out of $- x \cdot 15$ .

$\frac{x \cdot 16 + x (- 1 \cdot 15)}{15} + \frac{6}{5} = 1$

Step 3.1.5.1.1.3

Factor $x$ out of $x \cdot 16 + x (- 1 \cdot 15)$ .

$\frac{x (16 - 1 \cdot 15)}{15} + \frac{6}{5} = 1$

Step 3.1.5.1.2

Multiply $- 1$ by $15$ .

$\frac{x (16 - 15)}{15} + \frac{6}{5} = 1$

Step 3.1.5.1.3

Subtract $15$ from $16$ .

$\frac{x \cdot 1}{15} + \frac{6}{5} = 1$

Step 3.1.5.2

Multiply $x$ by $1$ .

$\frac{x}{15} + \frac{6}{5} = 1$

Step 3.2

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

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Step 3.2.1

Subtract $\frac{6}{5}$ from both sides of the equation.

$\frac{x}{15} = 1 - \frac{6}{5}$

Step 3.2.2

Write $1$ as a fraction with a common denominator.

$\frac{x}{15} = \frac{5}{5} - \frac{6}{5}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{x}{15} = \frac{5 - 6}{5}$

Step 3.2.4

Subtract $6$ from $5$ .

$\frac{x}{15} = \frac{- 1}{5}$

Step 3.2.5

Move the negative in front of the fraction.

$\frac{x}{15} = - \frac{1}{5}$

Step 3.3

Multiply both sides of the equation by $15$ .

$15 \frac{x}{15} = 15 (- \frac{1}{5})$

Step 3.4

Simplify both sides of the equation.

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Step 3.4.1

Simplify the left side.

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Step 3.4.1.1

Cancel the common factor of $15$ .

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Step 3.4.1.1.1

Cancel the common factor.

$15 \frac{x}{15} = 15 (- \frac{1}{5})$

Step 3.4.1.1.2

Rewrite the expression.

$x = 15 (- \frac{1}{5})$

Step 3.4.2

Simplify the right side.

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Step 3.4.2.1

Simplify $15 (- \frac{1}{5})$ .

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Step 3.4.2.1.1

Cancel the common factor of $5$ .

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Step 3.4.2.1.1.1

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$x = 15 (\frac{- 1}{5})$

Step 3.4.2.1.1.2

Factor $5$ out of $15$ .

$x = 5 (3) \frac{- 1}{5}$

Step 3.4.2.1.1.3

Cancel the common factor.

$x = 5 \cdot 3 \frac{- 1}{5}$

Step 3.4.2.1.1.4

Rewrite the expression.

$x = 3 \cdot - 1$

Step 3.4.2.1.2

Multiply $3$ by $- 1$ .

$x = - 3$