Solve for x x/3-(7x)/12=2/3

$\frac{x}{3} - \frac{7 x}{12} = \frac{2}{3}$

Step 1

Simplify $\frac{x}{3} - \frac{7 x}{12}$ .

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{3} \cdot \frac{4}{4} - \frac{7 x}{12} = \frac{2}{3}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{3}$ by $\frac{4}{4}$ .

$\frac{x \cdot 4}{3 \cdot 4} - \frac{7 x}{12} = \frac{2}{3}$

Multiply $3$ by $4$ .

$\frac{x \cdot 4}{12} - \frac{7 x}{12} = \frac{2}{3}$

Combine the numerators over the common denominator.

$\frac{x \cdot 4 - 7 x}{12} = \frac{2}{3}$

Simplify the numerator.

Move $4$ to the left of $x$ .

$\frac{4 \cdot x - 7 x}{12} = \frac{2}{3}$

Subtract $7 x$ from $4 x$ .

$\frac{- 3 x}{12} = \frac{2}{3}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $- 3$ and $12$ .

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

$\frac{3 (- x)}{12} = \frac{2}{3}$

Cancel the common factors.

Factor $3$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{- x}{4} = \frac{2}{3}$

Move the negative in front of the fraction.

$- \frac{x}{4} = \frac{2}{3}$

Step 2

Multiply both sides of the equation by $- 4$ .

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

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 4 (- \frac{x}{4})$ .

Cancel the common factor of $4$ .

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

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

Factor $4$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply.

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

Simplify the right side.

Simplify $- 4 (\frac{2}{3})$ .

Multiply $- 4 (\frac{2}{3})$ .

Combine $- 4$ and $\frac{2}{3}$ .

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

Multiply $- 4$ by $2$ .

$x = \frac{- 8}{3}$

Move the negative in front of the fraction.

$x = - \frac{8}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{8}{3}$

Decimal Form:

$x = - 2.\overline{6}$

Mixed Number Form:

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

Solve for x x/3-(7x)/12=2/3

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