Solve for x x/4-(x+20)/15=1/2

$\frac{x}{4} - \frac{x + 20}{15} = \frac{1}{2}$

Simplify $\frac{x}{4} - \frac{x + 20}{15}$ .

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{x}{4} \cdot \frac{15}{15} - \frac{x + 20}{15} = \frac{1}{2}$

To write $- \frac{x + 20}{15}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{4} \cdot \frac{15}{15} - \frac{x + 20}{15} \cdot \frac{4}{4} = \frac{1}{2}$

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{4}$ by $\frac{15}{15}$ .

$\frac{x \cdot 15}{4 \cdot 15} - \frac{x + 20}{15} \cdot \frac{4}{4} = \frac{1}{2}$

Multiply $4$ by $15$ .

$\frac{x \cdot 15}{60} - \frac{x + 20}{15} \cdot \frac{4}{4} = \frac{1}{2}$

Multiply $\frac{x + 20}{15}$ by $\frac{4}{4}$ .

$\frac{x \cdot 15}{60} - \frac{(x + 20) \cdot 4}{15 \cdot 4} = \frac{1}{2}$

Multiply $15$ by $4$ .

$\frac{x \cdot 15}{60} - \frac{(x + 20) \cdot 4}{60} = \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{x \cdot 15 - (x + 20) \cdot 4}{60} = \frac{1}{2}$

Simplify the numerator.

Move $15$ to the left of $x$ .

$\frac{15 \cdot x - (x + 20) \cdot 4}{60} = \frac{1}{2}$

Apply the distributive property.

$\frac{15 x + (- x - 1 \cdot 20) \cdot 4}{60} = \frac{1}{2}$

Multiply $- 1$ by $20$ .

$\frac{15 x + (- x - 20) \cdot 4}{60} = \frac{1}{2}$

Apply the distributive property.

$\frac{15 x - x \cdot 4 - 20 \cdot 4}{60} = \frac{1}{2}$

Multiply $4$ by $- 1$ .

$\frac{15 x - 4 x - 20 \cdot 4}{60} = \frac{1}{2}$

Multiply $- 20$ by $4$ .

$\frac{15 x - 4 x - 80}{60} = \frac{1}{2}$

Subtract $4 x$ from $15 x$ .

$\frac{11 x - 80}{60} = \frac{1}{2}$

Multiply both sides by $60$ .

$\frac{11 x - 80}{60} \cdot 60 = \frac{1}{2} \cdot 60$

Simplify.

Simplify the left side.

Cancel the common factor of $60$ .

Cancel the common factor.

$\frac{11 x - 80}{60} \cdot 60 = \frac{1}{2} \cdot 60$

Rewrite the expression.

$11 x - 80 = \frac{1}{2} \cdot 60$

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $60$ .

$11 x - 80 = \frac{1}{2} \cdot (2 (30))$

Cancel the common factor.

$11 x - 80 = \frac{1}{2} \cdot (2 \cdot 30)$

Rewrite the expression.

$11 x - 80 = 30$

Solve for $x$ .

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

Add $80$ to both sides of the equation.

$11 x = 30 + 80$

Add $30$ and $80$ .

$11 x = 110$

Divide each term in $11 x = 110$ by $11$ and simplify.

Divide each term in $11 x = 110$ by $11$ .

$\frac{11 x}{11} = \frac{110}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{110}{11}$

Divide $x$ by $1$ .

$x = \frac{110}{11}$

Simplify the right side.

Divide $110$ by $11$ .

$x = 10$

Solve for x x/4-(x+20)/15=1/2

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