Simplify -3/5x+1/2x

$- \frac{3}{5} x + \frac{1}{2} x$

Step 1

Simplify each term.

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

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

Move $3$ to the left of $x$ .

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

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

$- \frac{3 x}{5} + \frac{x}{2}$

Step 2

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

$- \frac{3 x}{5} \cdot \frac{2}{2} + \frac{x}{2}$

Step 3

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

$- \frac{3 x}{5} \cdot \frac{2}{2} + \frac{x}{2} \cdot \frac{5}{5}$

Step 4

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

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

$- \frac{3 x \cdot 2}{5 \cdot 2} + \frac{x}{2} \cdot \frac{5}{5}$

Multiply $5$ by $2$ .

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

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

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

Multiply $2$ by $5$ .

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

Step 5

Combine the numerators over the common denominator.

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

Step 6

Simplify the numerator.

Factor $x$ out of $- 3 x \cdot 2 + x \cdot 5$ .

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

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

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

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

Factor $x$ out of $x (- 3 \cdot 2) + x (5)$ .

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

Multiply $- 3$ by $2$ .

$\frac{x (- 6 + 5)}{10}$

Add $- 6$ and $5$ .

$\frac{x \cdot - 1}{10}$

Step 7

Simplify the expression.

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{10}$

Move the negative in front of the fraction.

$- \frac{x}{10}$

Simplify -3/5x+1/2x

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