Solve for x 2/3x-5/6x-3=1/2x-5

$\frac{2}{3} x - \frac{5}{6} x - 3 = \frac{1}{2} x - 5$

Step 1

Simplify $\frac{2}{3} x - \frac{5}{6} x - 3$ .

Simplify each term.

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

$\frac{2 x}{3} - \frac{5}{6} x - 3 = \frac{1}{2} x - 5$

Combine $x$ and $\frac{5}{6}$ .

$\frac{2 x}{3} - \frac{x \cdot 5}{6} - 3 = \frac{1}{2} x - 5$

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

$\frac{2 x}{3} - \frac{5 x}{6} - 3 = \frac{1}{2} x - 5$

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

$\frac{2 x}{3} \cdot \frac{2}{2} - \frac{5 x}{6} - 3 = \frac{1}{2} x - 5$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{2 x \cdot 2}{3 \cdot 2} - \frac{5 x}{6} - 3 = \frac{1}{2} x - 5$

Multiply $3$ by $2$ .

$\frac{2 x \cdot 2}{6} - \frac{5 x}{6} - 3 = \frac{1}{2} x - 5$

Combine the numerators over the common denominator.

$\frac{2 x \cdot 2 - 5 x}{6} - 3 = \frac{1}{2} x - 5$

Simplify each term.

Simplify the numerator.

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

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

$\frac{x (2 \cdot 2) - 5 x}{6} - 3 = \frac{1}{2} x - 5$

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

$\frac{x (2 \cdot 2) + x \cdot - 5}{6} - 3 = \frac{1}{2} x - 5$

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

$\frac{x (2 \cdot 2 - 5)}{6} - 3 = \frac{1}{2} x - 5$

Multiply $2$ by $2$ .

$\frac{x (4 - 5)}{6} - 3 = \frac{1}{2} x - 5$

Subtract $5$ from $4$ .

$\frac{x \cdot - 1}{6} - 3 = \frac{1}{2} x - 5$

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

$\frac{- 1 \cdot x}{6} - 3 = \frac{1}{2} x - 5$

Move the negative in front of the fraction.

$- \frac{x}{6} - 3 = \frac{1}{2} x - 5$

Step 2

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

$- \frac{x}{6} - 3 = \frac{x}{2} - 5$

Step 3

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

Subtract $\frac{x}{2}$ from both sides of the equation.

$- \frac{x}{6} - 3 - \frac{x}{2} = - 5$

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

$- \frac{x}{6} - \frac{x}{2} \cdot \frac{3}{3} - 3 = - 5$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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

$- \frac{x}{6} - \frac{x \cdot 3}{2 \cdot 3} - 3 = - 5$

Multiply $2$ by $3$ .

$- \frac{x}{6} - \frac{x \cdot 3}{6} - 3 = - 5$

Combine the numerators over the common denominator.

$\frac{- x - x \cdot 3}{6} - 3 = - 5$

Simplify each term.

Simplify the numerator.

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

Factor $x$ out of $- x$ .

$\frac{x \cdot - 1 - x \cdot 3}{6} - 3 = - 5$

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

$\frac{x \cdot - 1 + x (- 1 \cdot 3)}{6} - 3 = - 5$

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

$\frac{x (- 1 - 1 \cdot 3)}{6} - 3 = - 5$

Multiply $- 1$ by $3$ .

$\frac{x (- 1 - 3)}{6} - 3 = - 5$

Subtract $3$ from $- 1$ .

$\frac{x \cdot - 4}{6} - 3 = - 5$

Cancel the common factor of $- 4$ and $6$ .

Factor $2$ out of $x \cdot - 4$ .

$\frac{2 (x \cdot - 2)}{6} - 3 = - 5$

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Move the negative in front of the fraction.

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

Step 4

Move all terms not containing $x$ to the right side of the equation.

Add $3$ to both sides of the equation.

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

Add $- 5$ and $3$ .

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

Step 5

Multiply both sides of the equation by $- \frac{3}{2}$ .

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

Step 6

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{2} (- \frac{2 x}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

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

Move the leading negative in $- \frac{2 x}{3}$ into the numerator.

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

Factor $3$ out of $- 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

Simplify $- \frac{3}{2} \cdot - 2$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{2}$ into the numerator.

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

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = - 3 \cdot - 1$

Multiply $- 3$ by $- 1$ .

$x = 3$

Solve for x 2/3x-5/6x-3=1/2x-5

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