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

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

Step 1

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

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

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

Factor $x$ out of $3 x$ .

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

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

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

Factor $x$ out of $x \cdot 3 + x (- 1 \cdot 5)$ .

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

Multiply $- 1$ by $5$ .

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

Subtract $5$ from $3$ .

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

Simplify the expression.

Move $- 2$ to the left of $x$ .

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

Move the negative in front of the fraction.

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

Step 2

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

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

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

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

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

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

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

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

Multiply $5$ by $2$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

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

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

Factor $x$ out of $- x$ .

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

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

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

Multiply $- 2$ by $2$ .

$\frac{x (- 4 - 1)}{10} = - \frac{5}{2}$

Subtract $1$ from $- 4$ .

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

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

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

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

Cancel the common factors.

Factor $5$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Move the negative in front of the fraction.

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

Step 3

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

$- x = - 5$

Step 4

Divide each term in $- x = - 5$ by $- 1$ and simplify.

Divide each term in $- x = - 5$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 5$ by $- 1$ .

$x = 5$

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

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