Solve the Rational Equation for x x3/2=64

$x \frac{3}{2} = 64$

Step 1

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

$\frac{x \cdot 3}{2} = 64$

Step 2

Multiply each term in $\frac{x \cdot 3}{2} = 64$ by $\frac{2}{3}$ to eliminate the fractions.

Multiply each term in $\frac{x \cdot 3}{2} = 64$ by $\frac{2}{3}$ .

$\frac{x \cdot 3}{2} \cdot \frac{2}{3} = 64 (\frac{2}{3})$

Simplify the left side.

Cancel the common factor of $3$ .

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

$\frac{3 \cdot x}{2} \cdot \frac{2}{3} = 64 (\frac{2}{3})$

Cancel the common factor.

$\frac{3 \cdot x}{2} \cdot \frac{2}{3} = 64 (\frac{2}{3})$

Rewrite the expression.

$\frac{x}{2} \cdot 2 = 64 (\frac{2}{3})$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{x}{2} \cdot 2 = 64 (\frac{2}{3})$

Rewrite the expression.

$x = 64 (\frac{2}{3})$

Simplify the right side.

Multiply $64 (\frac{2}{3})$ .

Combine $64$ and $\frac{2}{3}$ .

$x = \frac{64 \cdot 2}{3}$

Multiply $64$ by $2$ .

$x = \frac{128}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{128}{3}$

Decimal Form:

$x = 42.\overline{6}$

Mixed Number Form:

$x = 42 \frac{2}{3}$