Finite Math Examples

$\frac{3 x}{5} - x = \frac{x}{15} - \frac{35}{3}$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $\frac{x}{15}$ from both sides of the equation.

$\frac{3 x}{5} - x - \frac{x}{15} = - \frac{35}{3}$

Step 1.2

Add $\frac{35}{3}$ to both sides of the equation.

$\frac{3 x}{5} - x - \frac{x}{15} + \frac{35}{3} = 0$

Step 2

Simplify $\frac{3 x}{5} - x - \frac{x}{15} + \frac{35}{3}$ .

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Step 2.1

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

$\frac{3 x}{5} - x \cdot \frac{5}{5} - \frac{x}{15} + \frac{35}{3} = 0$

Step 2.2

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

$\frac{3 x}{5} + \frac{- x \cdot 5}{5} - \frac{x}{15} + \frac{35}{3} = 0$

Step 2.3

Combine the numerators over the common denominator.

$\frac{3 x - x \cdot 5}{5} - \frac{x}{15} + \frac{35}{3} = 0$

Step 2.4

Simplify each term.

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Step 2.4.1

Simplify the numerator.

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Step 2.4.1.1

Factor $x$ out of $3 x - x \cdot 5$ .

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Step 2.4.1.1.1

Factor $x$ out of $3 x$ .

$\frac{x \cdot 3 - x \cdot 5}{5} - \frac{x}{15} + \frac{35}{3} = 0$

Step 2.4.1.1.2

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

$\frac{x \cdot 3 + x (- 1 \cdot 5)}{5} - \frac{x}{15} + \frac{35}{3} = 0$

Step 2.4.1.1.3

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

$\frac{x (3 - 1 \cdot 5)}{5} - \frac{x}{15} + \frac{35}{3} = 0$

Step 2.4.1.2

Multiply $- 1$ by $5$ .

$\frac{x (3 - 5)}{5} - \frac{x}{15} + \frac{35}{3} = 0$

Step 2.4.1.3

Subtract $5$ from $3$ .

$\frac{x \cdot - 2}{5} - \frac{x}{15} + \frac{35}{3} = 0$

Step 2.4.2

Move $- 2$ to the left of $x$ .

$\frac{- 2 \cdot x}{5} - \frac{x}{15} + \frac{35}{3} = 0$

Step 2.4.3

Move the negative in front of the fraction.

$- \frac{2 x}{5} - \frac{x}{15} + \frac{35}{3} = 0$

Step 2.5

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

$- \frac{2 x}{5} \cdot \frac{3}{3} - \frac{x}{15} + \frac{35}{3} = 0$

Step 2.6

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

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Step 2.6.1

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

$- \frac{2 x \cdot 3}{5 \cdot 3} - \frac{x}{15} + \frac{35}{3} = 0$

Step 2.6.2

Multiply $5$ by $3$ .

$- \frac{2 x \cdot 3}{15} - \frac{x}{15} + \frac{35}{3} = 0$

Step 2.7

Combine the numerators over the common denominator.

$\frac{- 2 x \cdot 3 - x}{15} + \frac{35}{3} = 0$

Step 2.8

Simplify each term.

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Step 2.8.1

Simplify the numerator.

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Step 2.8.1.1

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

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Step 2.8.1.1.1

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

$\frac{x (- 2 \cdot 3) - x}{15} + \frac{35}{3} = 0$

Step 2.8.1.1.2

Factor $x$ out of $- x$ .

$\frac{x (- 2 \cdot 3) + x \cdot - 1}{15} + \frac{35}{3} = 0$

Step 2.8.1.1.3

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

$\frac{x (- 2 \cdot 3 - 1)}{15} + \frac{35}{3} = 0$

Step 2.8.1.2

Multiply $- 2$ by $3$ .

$\frac{x (- 6 - 1)}{15} + \frac{35}{3} = 0$

Step 2.8.1.3

Subtract $1$ from $- 6$ .

$\frac{x \cdot - 7}{15} + \frac{35}{3} = 0$

Step 2.8.2

Move $- 7$ to the left of $x$ .

$\frac{- 7 \cdot x}{15} + \frac{35}{3} = 0$

Step 2.8.3

Move the negative in front of the fraction.

$- \frac{7 x}{15} + \frac{35}{3} = 0$

Step 3

To write $\frac{35}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{7 x}{15} + \frac{35}{3} \cdot \frac{5}{5} = 0$

Step 4

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

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Step 4.1

Multiply $\frac{35}{3}$ by $\frac{5}{5}$ .

$- \frac{7 x}{15} + \frac{35 \cdot 5}{3 \cdot 5} = 0$

Step 4.2

Multiply $3$ by $5$ .

$- \frac{7 x}{15} + \frac{35 \cdot 5}{15} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{- 7 x + 35 \cdot 5}{15} = 0$

Step 6

Simplify the numerator.

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Step 6.1

Factor $7$ out of $- 7 x + 35 \cdot 5$ .

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Step 6.1.1

Factor $7$ out of $- 7 x$ .

$\frac{7 (- x) + 35 \cdot 5}{15} = 0$

Step 6.1.2

Factor $7$ out of $35 \cdot 5$ .

$\frac{7 (- x) + 7 (5 \cdot 5)}{15} = 0$

Step 6.1.3

Factor $7$ out of $7 (- x) + 7 (5 \cdot 5)$ .

$\frac{7 (- x + 5 \cdot 5)}{15} = 0$

Step 6.2

Multiply $5$ by $5$ .

$\frac{7 (- x + 25)}{15} = 0$

Step 7

Set the numerator equal to zero.

$7 (- x + 25) = 0$

Step 8

Solve the equation for $x$ .

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Step 8.1

Divide each term in $7 (- x + 25) = 0$ by $7$ and simplify.

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Step 8.1.1

Divide each term in $7 (- x + 25) = 0$ by $7$ .

$\frac{7 (- x + 25)}{7} = \frac{0}{7}$

Step 8.1.2

Simplify the left side.

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Step 8.1.2.1

Cancel the common factor of $7$ .

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Step 8.1.2.1.1

Cancel the common factor.

$\frac{7 (- x + 25)}{7} = \frac{0}{7}$

Step 8.1.2.1.2

Divide $- x + 25$ by $1$ .

$- x + 25 = \frac{0}{7}$

Step 8.1.3

Simplify the right side.

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Step 8.1.3.1

Divide $0$ by $7$ .

$- x + 25 = 0$

Step 8.2

Subtract $25$ from both sides of the equation.

$- x = - 25$

Step 8.3

Divide each term in $- x = - 25$ by $- 1$ and simplify.

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Step 8.3.1

Divide each term in $- x = - 25$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 25}{- 1}$

Step 8.3.2

Simplify the left side.

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Step 8.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 25}{- 1}$

Step 8.3.2.2

Divide $x$ by $1$ .

$x = \frac{- 25}{- 1}$

Step 8.3.3

Simplify the right side.

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Step 8.3.3.1

Divide $- 25$ by $- 1$ .

$x = 25$