Solve for x (3x)/2+5/8=x/4

$\frac{3 x}{2} + \frac{5}{8} = \frac{x}{4}$

Multiply both sides by $4$ .

$(\frac{3 x}{2} + \frac{5}{8}) \cdot 4 = \frac{x}{4} \cdot 4$

Simplify.

Simplify the left side.

Simplify $(\frac{3 x}{2} + \frac{5}{8}) \cdot 4$ .

Apply the distributive property.

$\frac{3 x}{2} \cdot 4 + \frac{5}{8} \cdot 4 = \frac{x}{4} \cdot 4$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$\frac{3 x}{2} \cdot (2 (2)) + \frac{5}{8} \cdot 4 = \frac{x}{4} \cdot 4$

Cancel the common factor.

$\frac{3 x}{2} \cdot (2 \cdot 2) + \frac{5}{8} \cdot 4 = \frac{x}{4} \cdot 4$

Rewrite the expression.

$3 x \cdot 2 + \frac{5}{8} \cdot 4 = \frac{x}{4} \cdot 4$

Multiply $2$ by $3$ .

$6 x + \frac{5}{8} \cdot 4 = \frac{x}{4} \cdot 4$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$6 x + \frac{5}{4 (2)} \cdot 4 = \frac{x}{4} \cdot 4$

Cancel the common factor.

$6 x + \frac{5}{4 \cdot 2} \cdot 4 = \frac{x}{4} \cdot 4$

Rewrite the expression.

$6 x + \frac{5}{2} = \frac{x}{4} \cdot 4$

Simplify the right side.

Cancel the common factor of $4$ .

Cancel the common factor.

$6 x + \frac{5}{2} = \frac{x}{4} \cdot 4$

Rewrite the expression.

$6 x + \frac{5}{2} = x$

Solve for $x$ .

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

Subtract $x$ from both sides of the equation.

$6 x + \frac{5}{2} - x = 0$

Subtract $x$ from $6 x$ .

$5 x + \frac{5}{2} = 0$

Subtract $\frac{5}{2}$ from both sides of the equation.

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

Divide each term in $5 x = - \frac{5}{2}$ by $5$ and simplify.

Divide each term in $5 x = - \frac{5}{2}$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

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

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

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

Factor $5$ out of $- 5$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.5$

Solve for x (3x)/2+5/8=x/4

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