Solve for x 5/6x-2/3x=-3/8

$\frac{5}{6} x - \frac{2}{3} x = - \frac{3}{8}$

Step 1

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

Simplify each term.

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

$\frac{5 x}{6} - \frac{2}{3} x = - \frac{3}{8}$

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

$\frac{5 x}{6} - \frac{x \cdot 2}{3} = - \frac{3}{8}$

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

$\frac{5 x}{6} - \frac{2 x}{3} = - \frac{3}{8}$

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

$\frac{5 x}{6} - \frac{2 x}{3} \cdot \frac{2}{2} = - \frac{3}{8}$

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

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

$\frac{5 x}{6} - \frac{2 x \cdot 2}{3 \cdot 2} = - \frac{3}{8}$

Multiply $3$ by $2$ .

$\frac{5 x}{6} - \frac{2 x \cdot 2}{6} = - \frac{3}{8}$

Combine the numerators over the common denominator.

$\frac{5 x - 2 x \cdot 2}{6} = - \frac{3}{8}$

Simplify the numerator.

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

Factor $x$ out of $5 x$ .

$\frac{x \cdot 5 - 2 x \cdot 2}{6} = - \frac{3}{8}$

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

$\frac{x \cdot 5 + x (- 2 \cdot 2)}{6} = - \frac{3}{8}$

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

$\frac{x (5 - 2 \cdot 2)}{6} = - \frac{3}{8}$

Multiply $- 2$ by $2$ .

$\frac{x (5 - 4)}{6} = - \frac{3}{8}$

Subtract $4$ from $5$ .

$\frac{x \cdot 1}{6} = - \frac{3}{8}$

Multiply $x$ by $1$ .

$\frac{x}{6} = - \frac{3}{8}$

Step 2

Multiply both sides of the equation by $6$ .

$6 \frac{x}{6} = 6 (- \frac{3}{8})$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$6 \frac{x}{6} = 6 (- \frac{3}{8})$

Rewrite the expression.

$x = 6 (- \frac{3}{8})$

Simplify the right side.

Simplify $6 (- \frac{3}{8})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{8}$ into the numerator.

$x = 6 (\frac{- 3}{8})$

Factor $2$ out of $6$ .

$x = 2 (3) \frac{- 3}{8}$

Factor $2$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Simplify the expression.

Multiply $3$ by $- 3$ .

$x = \frac{- 9}{4}$

Move the negative in front of the fraction.

$x = - \frac{9}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{9}{4}$

Decimal Form:

$x = - 2.25$

Mixed Number Form:

$x = - 2 \frac{1}{4}$

Solve for x 5/6x-2/3x=-3/8

Related Questions

Support LCMGCF.com by disabling your adblocker.