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

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

Step 1

Combine $\frac{1}{2}$ and $x$ .

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

Step 2

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

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

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

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

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

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $5$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 3$ by $2$ .

$\frac{x}{2} = \frac{1 - 6}{10}$

Subtract $6$ from $1$ .

$\frac{x}{2} = \frac{- 5}{10}$

Cancel the common factor of $- 5$ and $10$ .

Factor $5$ out of $- 5$ .

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

Cancel the common factors.

Factor $5$ out of $10$ .

$\frac{x}{2} = \frac{5 \cdot - 1}{5 \cdot 2}$

Cancel the common factor.

$\frac{x}{2} = \frac{5 \cdot - 1}{5 \cdot 2}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x = - 1$