Solve for x 1/2(2/3x+10)=3/5x+1

$\frac{1}{2} (\frac{2}{3} x + 10) = \frac{3}{5} x + 1$

Simplify $\frac{1}{2} \cdot (\frac{2}{3} x + 10)$ .

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (\frac{2}{3} x + 10) = \frac{3}{5} x + 1$

Simplify by adding zeros.

$\frac{1}{2} \cdot (\frac{2}{3} x + 10) = \frac{3}{5} x + 1$

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

$\frac{1}{2} \cdot (\frac{2 x}{3} + 10) = \frac{3}{5} x + 1$

Apply the distributive property.

$\frac{1}{2} \cdot \frac{2 x}{3} + \frac{1}{2} \cdot 10 = \frac{3}{5} x + 1$

Cancel the common factor of $2$ .

Factor $2$ out of $2 x$ .

$\frac{1}{2} \cdot \frac{2 (x)}{3} + \frac{1}{2} \cdot 10 = \frac{3}{5} x + 1$

Cancel the common factor.

$\frac{1}{2} \cdot \frac{2 x}{3} + \frac{1}{2} \cdot 10 = \frac{3}{5} x + 1$

Rewrite the expression.

$\frac{x}{3} + \frac{1}{2} \cdot 10 = \frac{3}{5} x + 1$

Cancel the common factor of $2$ .

Factor $2$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x}{3} + 5 = \frac{3}{5} x + 1$

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

$\frac{x}{3} + 5 = \frac{3 x}{5} + 1$

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

Subtract $\frac{3 x}{5}$ from both sides of the equation.

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

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

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

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

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

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

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

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

Multiply $3$ by $5$ .

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

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

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

Multiply $5$ by $3$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

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

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

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

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

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

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

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

Multiply $- 3$ by $3$ .

$\frac{x (5 - 9)}{15} + 5 = 1$

Subtract $9$ from $5$ .

$\frac{x \cdot - 4}{15} + 5 = 1$

Move $- 4$ to the left of $x$ .

$\frac{- 4 \cdot x}{15} + 5 = 1$

Move the negative in front of the fraction.

$- \frac{4 x}{15} + 5 = 1$

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

Subtract $5$ from both sides of the equation.

$- \frac{4 x}{15} = 1 - 5$

Subtract $5$ from $1$ .

$- \frac{4 x}{15} = - 4$

Multiply both sides of the equation by $- \frac{15}{4}$ .

$- \frac{15}{4} (- \frac{4 x}{15}) = - \frac{15}{4} \cdot - 4$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{15}{4} (- \frac{4 x}{15})$ .

Cancel the common factor of $15$ .

Move the leading negative in $- \frac{15}{4}$ into the numerator.

$\frac{- 15}{4} (- \frac{4 x}{15}) = - \frac{15}{4} \cdot - 4$

Move the leading negative in $- \frac{4 x}{15}$ into the numerator.

$\frac{- 15}{4} \cdot \frac{- 4 x}{15} = - \frac{15}{4} \cdot - 4$

Factor $15$ out of $- 15$ .

$\frac{15 (- 1)}{4} \cdot \frac{- 4 x}{15} = - \frac{15}{4} \cdot - 4$

Cancel the common factor.

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

Rewrite the expression.

$\frac{- 1}{4} (- 4 x) = - \frac{15}{4} \cdot - 4$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4 x$ .

$\frac{- 1}{4} (4 (- x)) = - \frac{15}{4} \cdot - 4$

Cancel the common factor.

$\frac{- 1}{4} (4 (- x)) = - \frac{15}{4} \cdot - 4$

Rewrite the expression.

$- - x = - \frac{15}{4} \cdot - 4$

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

$x = - \frac{15}{4} \cdot - 4$

Simplify the right side.

Simplify $- \frac{15}{4} \cdot - 4$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{15}{4}$ into the numerator.

$x = \frac{- 15}{4} \cdot - 4$

Factor $4$ out of $- 4$ .

$x = \frac{- 15}{4} \cdot (4 (- 1))$

Cancel the common factor.

$x = \frac{- 15}{4} \cdot (4 \cdot - 1)$

Rewrite the expression.

$x = - 15 \cdot - 1$

Multiply $- 15$ by $- 1$ .

$x = 15$

Solve for x 1/2(2/3x+10)=3/5x+1

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