Solve for x 3x-(2x)/5=x/10-7/4

$3 x - \frac{2 x}{5} = \frac{x}{10} - \frac{7}{4}$

Simplify $3 x - \frac{2 x}{5}$ .

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

$3 x \cdot \frac{5}{5} - \frac{2 x}{5} = \frac{x}{10} - \frac{7}{4}$

Simplify terms.

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

$\frac{3 x \cdot 5}{5} - \frac{2 x}{5} = \frac{x}{10} - \frac{7}{4}$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 5 - 2 x}{5} = \frac{x}{10} - \frac{7}{4}$

Simplify the numerator.

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

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

$\frac{x (3 \cdot 5) - 2 x}{5} = \frac{x}{10} - \frac{7}{4}$

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

$\frac{x (3 \cdot 5) + x \cdot - 2}{5} = \frac{x}{10} - \frac{7}{4}$

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

$\frac{x (3 \cdot 5 - 2)}{5} = \frac{x}{10} - \frac{7}{4}$

Multiply $3$ by $5$ .

$\frac{x (15 - 2)}{5} = \frac{x}{10} - \frac{7}{4}$

Subtract $2$ from $15$ .

$\frac{x \cdot 13}{5} = \frac{x}{10} - \frac{7}{4}$

Move $13$ to the left of $x$ .

$\frac{13 x}{5} = \frac{x}{10} - \frac{7}{4}$

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

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

$\frac{13 x}{5} - \frac{x}{10} = - \frac{7}{4}$

To write $\frac{13 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{13 x}{5} \cdot \frac{2}{2} - \frac{x}{10} = - \frac{7}{4}$

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

Multiply $\frac{13 x}{5}$ by $\frac{2}{2}$ .

$\frac{13 x \cdot 2}{5 \cdot 2} - \frac{x}{10} = - \frac{7}{4}$

Multiply $5$ by $2$ .

$\frac{13 x \cdot 2}{10} - \frac{x}{10} = - \frac{7}{4}$

Combine the numerators over the common denominator.

$\frac{13 x \cdot 2 - x}{10} = - \frac{7}{4}$

Simplify the numerator.

Factor $x$ out of $13 x \cdot 2 - x$ .

Factor $x$ out of $13 x \cdot 2$ .

$\frac{x (13 \cdot 2) - x}{10} = - \frac{7}{4}$

Factor $x$ out of $- x$ .

$\frac{x (13 \cdot 2) + x \cdot - 1}{10} = - \frac{7}{4}$

Factor $x$ out of $x (13 \cdot 2) + x \cdot - 1$ .

$\frac{x (13 \cdot 2 - 1)}{10} = - \frac{7}{4}$

Multiply $13$ by $2$ .

$\frac{x (26 - 1)}{10} = - \frac{7}{4}$

Subtract $1$ from $26$ .

$\frac{x \cdot 25}{10} = - \frac{7}{4}$

Cancel the common factor of $25$ and $10$ .

Factor $5$ out of $x \cdot 25$ .

$\frac{5 (x \cdot 5)}{10} = - \frac{7}{4}$

Cancel the common factors.

Factor $5$ out of $10$ .

$\frac{5 (x \cdot 5)}{5 (2)} = - \frac{7}{4}$

Cancel the common factor.

$\frac{5 (x \cdot 5)}{5 \cdot 2} = - \frac{7}{4}$

Rewrite the expression.

$\frac{x \cdot 5}{2} = - \frac{7}{4}$

Move $5$ to the left of $x$ .

$\frac{5 x}{2} = - \frac{7}{4}$

Multiply both sides of the equation by $\frac{2}{5}$ .

$\frac{2}{5} \cdot \frac{5 x}{2} = \frac{2}{5} (- \frac{7}{4})$

Simplify both sides of the equation.

Simplify the left side.

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

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{5} \cdot \frac{5 x}{2} = \frac{2}{5} (- \frac{7}{4})$

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{2}{5} (- \frac{7}{4})$

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{2}{5} (- \frac{7}{4})$

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{2}{5} (- \frac{7}{4})$

Rewrite the expression.

$x = \frac{2}{5} (- \frac{7}{4})$

Simplify the right side.

Simplify $\frac{2}{5} (- \frac{7}{4})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{7}{4}$ into the numerator.

$x = \frac{2}{5} \cdot \frac{- 7}{4}$

Factor $2$ out of $4$ .

$x = \frac{2}{5} \cdot \frac{- 7}{2 (2)}$

Cancel the common factor.

$x = \frac{2}{5} \cdot \frac{- 7}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{1}{5} \cdot \frac{- 7}{2}$

Multiply $\frac{1}{5}$ by $\frac{- 7}{2}$ .

$x = \frac{- 7}{5 \cdot 2}$

Simplify the expression.

Multiply $5$ by $2$ .

$x = \frac{- 7}{10}$

Move the negative in front of the fraction.

$x = - \frac{7}{10}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{7}{10}$

Decimal Form:

$x = - 0.7$

Solve for x 3x-(2x)/5=x/10-7/4

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