Solve for x 2/3x-1/5x=x-1

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

Simplify $\frac{2}{3} x - \frac{1}{5} x$ .

Simplify each term.

Combine $\frac{2}{3}$ and $x$ .

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

Combine $x$ and $\frac{1}{5}$ .

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

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

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

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

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

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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

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

Multiply $3$ by $5$ .

$\frac{2 x \cdot 5}{15} - \frac{x}{5} \cdot \frac{3}{3} = x - 1$

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

$\frac{2 x \cdot 5}{15} - \frac{x \cdot 3}{5 \cdot 3} = x - 1$

Multiply $5$ by $3$ .

$\frac{2 x \cdot 5}{15} - \frac{x \cdot 3}{15} = x - 1$

Combine the numerators over the common denominator.

$\frac{2 x \cdot 5 - x \cdot 3}{15} = x - 1$

Simplify the numerator.

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

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

$\frac{x (2 \cdot 5) - x \cdot 3}{15} = x - 1$

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

$\frac{x (2 \cdot 5) + x (- 1 \cdot 3)}{15} = x - 1$

Factor $x$ out of $x (2 \cdot 5) + x (- 1 \cdot 3)$ .

$\frac{x (2 \cdot 5 - 1 \cdot 3)}{15} = x - 1$

Multiply $2$ by $5$ .

$\frac{x (10 - 1 \cdot 3)}{15} = x - 1$

Multiply $- 1$ by $3$ .

$\frac{x (10 - 3)}{15} = x - 1$

Subtract $3$ from $10$ .

$\frac{x \cdot 7}{15} = x - 1$

Move $7$ to the left of $x$ .

$\frac{7 x}{15} = x - 1$

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

Subtract $x$ from both sides of the equation.

$\frac{7 x}{15} - x = - 1$

To write $- x$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$\frac{7 x}{15} - x \cdot \frac{15}{15} = - 1$

Combine $- x$ and $\frac{15}{15}$ .

$\frac{7 x}{15} + \frac{- x \cdot 15}{15} = - 1$

Combine the numerators over the common denominator.

$\frac{7 x - x \cdot 15}{15} = - 1$

Simplify the numerator.

Factor $x$ out of $7 x - x \cdot 15$ .

Factor $x$ out of $7 x$ .

$\frac{x \cdot 7 - x \cdot 15}{15} = - 1$

Factor $x$ out of $- x \cdot 15$ .

$\frac{x \cdot 7 + x (- 1 \cdot 15)}{15} = - 1$

Factor $x$ out of $x \cdot 7 + x (- 1 \cdot 15)$ .

$\frac{x (7 - 1 \cdot 15)}{15} = - 1$

Multiply $- 1$ by $15$ .

$\frac{x (7 - 15)}{15} = - 1$

Subtract $15$ from $7$ .

$\frac{x \cdot - 8}{15} = - 1$

Move $- 8$ to the left of $x$ .

$\frac{- 8 \cdot x}{15} = - 1$

Move the negative in front of the fraction.

$- \frac{8 x}{15} = - 1$

Multiply both sides of the equation by $- \frac{15}{8}$ .

$- \frac{15}{8} (- \frac{8 x}{15}) = - \frac{15}{8} \cdot - 1$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{15}{8} (- \frac{8 x}{15})$ .

Cancel the common factor of $15$ .

Move the leading negative in $- \frac{15}{8}$ into the numerator.

$\frac{- 15}{8} (- \frac{8 x}{15}) = - \frac{15}{8} \cdot - 1$

Move the leading negative in $- \frac{8 x}{15}$ into the numerator.

$\frac{- 15}{8} \cdot \frac{- 8 x}{15} = - \frac{15}{8} \cdot - 1$

Factor $15$ out of $- 15$ .

$\frac{15 (- 1)}{8} \cdot \frac{- 8 x}{15} = - \frac{15}{8} \cdot - 1$

Cancel the common factor.

$\frac{15 \cdot - 1}{8} \cdot \frac{- 8 x}{15} = - \frac{15}{8} \cdot - 1$

Rewrite the expression.

$\frac{- 1}{8} (- 8 x) = - \frac{15}{8} \cdot - 1$

Cancel the common factor of $8$ .

Factor $8$ out of $- 8 x$ .

$\frac{- 1}{8} (8 (- x)) = - \frac{15}{8} \cdot - 1$

Cancel the common factor.

$\frac{- 1}{8} (8 (- x)) = - \frac{15}{8} \cdot - 1$

Rewrite the expression.

$- - x = - \frac{15}{8} \cdot - 1$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{15}{8} \cdot - 1$

Multiply $x$ by $1$ .

$x = - \frac{15}{8} \cdot - 1$

Simplify the right side.

Multiply $- \frac{15}{8} \cdot - 1$ .

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{15}{8})$

Multiply $\frac{15}{8}$ by $1$ .

$x = \frac{15}{8}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{15}{8}$

Decimal Form:

$x = 1.875$

Mixed Number Form:

$x = 1 \frac{7}{8}$

Solve for x 2/3x-1/5x=x-1

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