Solve for x (3x)/8-(5x)/8=-x/6-21/4

$\frac{3 x}{8} - \frac{5 x}{8} = - \frac{x}{6} - \frac{21}{4}$

Simplify $\frac{3 x}{8} - \frac{5 x}{8}$ .

Combine the numerators over the common denominator.

$\frac{3 x - 5 x}{8} = - \frac{x}{6} - \frac{21}{4}$

Subtract $5 x$ from $3 x$ .

$\frac{- 2 x}{8} = - \frac{x}{6} - \frac{21}{4}$

Cancel the common factor of $- 2$ and $8$ .

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

$\frac{2 (- x)}{8} = - \frac{x}{6} - \frac{21}{4}$

Cancel the common factors.

Factor $2$ out of $8$ .

$\frac{2 (- x)}{2 (4)} = - \frac{x}{6} - \frac{21}{4}$

Cancel the common factor.

$\frac{2 (- x)}{2 \cdot 4} = - \frac{x}{6} - \frac{21}{4}$

Rewrite the expression.

$\frac{- x}{4} = - \frac{x}{6} - \frac{21}{4}$

Move the negative in front of the fraction.

$- \frac{x}{4} = - \frac{x}{6} - \frac{21}{4}$

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

Add $\frac{x}{6}$ to both sides of the equation.

$- \frac{x}{4} + \frac{x}{6} = - \frac{21}{4}$

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

$- \frac{x}{4} \cdot \frac{3}{3} + \frac{x}{6} = - \frac{21}{4}$

To write $\frac{x}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{x}{4} \cdot \frac{3}{3} + \frac{x}{6} \cdot \frac{2}{2} = - \frac{21}{4}$

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

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

$- \frac{x \cdot 3}{4 \cdot 3} + \frac{x}{6} \cdot \frac{2}{2} = - \frac{21}{4}$

Multiply $4$ by $3$ .

$- \frac{x \cdot 3}{12} + \frac{x}{6} \cdot \frac{2}{2} = - \frac{21}{4}$

Multiply $\frac{x}{6}$ by $\frac{2}{2}$ .

$- \frac{x \cdot 3}{12} + \frac{x \cdot 2}{6 \cdot 2} = - \frac{21}{4}$

Multiply $6$ by $2$ .

$- \frac{x \cdot 3}{12} + \frac{x \cdot 2}{12} = - \frac{21}{4}$

Combine the numerators over the common denominator.

$\frac{- x \cdot 3 + x \cdot 2}{12} = - \frac{21}{4}$

Simplify the numerator.

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

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

$\frac{x (- 1 \cdot 3) + x \cdot 2}{12} = - \frac{21}{4}$

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

$\frac{x (- 1 \cdot 3) + x (2)}{12} = - \frac{21}{4}$

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

$\frac{x (- 1 \cdot 3 + 2)}{12} = - \frac{21}{4}$

Multiply $- 1$ by $3$ .

$\frac{x (- 3 + 2)}{12} = - \frac{21}{4}$

Add $- 3$ and $2$ .

$\frac{x \cdot - 1}{12} = - \frac{21}{4}$

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

$\frac{- 1 \cdot x}{12} = - \frac{21}{4}$

Move the negative in front of the fraction.

$- \frac{x}{12} = - \frac{21}{4}$

Multiply both sides of the equation by $- 12$ .

$- 12 (- \frac{x}{12}) = - 12 (- \frac{21}{4})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 12 (- \frac{x}{12})$ .

Cancel the common factor of $12$ .

Move the leading negative in $- \frac{x}{12}$ into the numerator.

$- 12 \frac{- x}{12} = - 12 (- \frac{21}{4})$

Factor $12$ out of $- 12$ .

$12 (- 1) \frac{- x}{12} = - 12 (- \frac{21}{4})$

Cancel the common factor.

$12 \cdot - 1 \frac{- x}{12} = - 12 (- \frac{21}{4})$

Rewrite the expression.

$- - x = - 12 (- \frac{21}{4})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 12 (- \frac{21}{4})$

Multiply $x$ by $1$ .

$x = - 12 (- \frac{21}{4})$

Simplify the right side.

Simplify $- 12 (- \frac{21}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{21}{4}$ into the numerator.

$x = - 12 (\frac{- 21}{4})$

Factor $4$ out of $- 12$ .

$x = 4 (- 3) \frac{- 21}{4}$

Cancel the common factor.

$x = 4 \cdot - 3 \frac{- 21}{4}$

Rewrite the expression.

$x = - 3 \cdot - 21$

Multiply $- 3$ by $- 21$ .

$x = 63$

Solve for x (3x)/8-(5x)/8=-x/6-21/4

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