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

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

Step 1

Simplify $\frac{x}{5} - \frac{x}{2}$ .

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

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

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

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

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

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

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

Multiply $5$ by $2$ .

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

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

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

Multiply $2$ by $5$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

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

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

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

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

Factor $x$ out of $x (2) + x (- 1 \cdot 5)$ .

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

Multiply $- 1$ by $5$ .

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

Subtract $5$ from $2$ .

$\frac{x \cdot - 3}{10} = 3 + \frac{3 x}{10}$

Simplify the expression.

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

$\frac{- 3 \cdot x}{10} = 3 + \frac{3 x}{10}$

Move the negative in front of the fraction.

$- \frac{3 x}{10} = 3 + \frac{3 x}{10}$

Step 2

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

Subtract $\frac{3 x}{10}$ from both sides of the equation.

$- \frac{3 x}{10} - \frac{3 x}{10} = 3$

Combine the numerators over the common denominator.

$\frac{- 3 x - 3 x}{10} = 3$

Subtract $3 x$ from $- 3 x$ .

$\frac{- 6 x}{10} = 3$

Cancel the common factor of $- 6$ and $10$ .

Factor $2$ out of $- 6 x$ .

$\frac{2 (- 3 x)}{10} = 3$

Cancel the common factors.

Factor $2$ out of $10$ .

$\frac{2 (- 3 x)}{2 (5)} = 3$

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 3

Multiply both sides of the equation by $- \frac{5}{3}$ .

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

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{5}{3} (- \frac{3 x}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{3}$ into the numerator.

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

Move the leading negative in $- \frac{3 x}{5}$ into the numerator.

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

Factor $5$ out of $- 5$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $3$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{5}{3}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

$x = - 5$

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

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