Solve for x 3/4x-8=x/3

$\frac{3}{4} x - 8 = \frac{x}{3}$

Step 1

Multiply both sides by $3$ .

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

Step 2

Simplify.

Simplify the left side.

Simplify $(\frac{3}{4} x - 8) \cdot 3$ .

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

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

Apply the distributive property.

$\frac{3 x}{4} \cdot 3 - 8 \cdot 3 = \frac{x}{3} \cdot 3$

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

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

$\frac{3 x \cdot 3}{4} - 8 \cdot 3 = \frac{x}{3} \cdot 3$

Multiply $3$ by $3$ .

$\frac{9 x}{4} - 8 \cdot 3 = \frac{x}{3} \cdot 3$

Multiply $- 8$ by $3$ .

$\frac{9 x}{4} - 24 = \frac{x}{3} \cdot 3$

Simplify the right side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{9 x}{4} - 24 = \frac{x}{3} \cdot 3$

Rewrite the expression.

$\frac{9 x}{4} - 24 = x$

Step 3

Solve for $x$ .

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

Subtract $x$ from both sides of the equation.

$\frac{9 x}{4} - 24 - x = 0$

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

$\frac{9 x}{4} - x \cdot \frac{4}{4} - 24 = 0$

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

$\frac{9 x}{4} + \frac{- x \cdot 4}{4} - 24 = 0$

Combine the numerators over the common denominator.

$\frac{9 x - x \cdot 4}{4} - 24 = 0$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $9 x - x \cdot 4$ .

Factor $x$ out of $9 x$ .

$\frac{x \cdot 9 - x \cdot 4}{4} - 24 = 0$

Factor $x$ out of $- x \cdot 4$ .

$\frac{x \cdot 9 + x (- 1 \cdot 4)}{4} - 24 = 0$

Factor $x$ out of $x \cdot 9 + x (- 1 \cdot 4)$ .

$\frac{x (9 - 1 \cdot 4)}{4} - 24 = 0$

Multiply $- 1$ by $4$ .

$\frac{x (9 - 4)}{4} - 24 = 0$

Subtract $4$ from $9$ .

$\frac{x \cdot 5}{4} - 24 = 0$

Move $5$ to the left of $x$ .

$\frac{5 x}{4} - 24 = 0$

Add $24$ to both sides of the equation.

$\frac{5 x}{4} = 24$

Multiply both sides of the equation by $\frac{4}{5}$ .

$\frac{4}{5} \cdot \frac{5 x}{4} = \frac{4}{5} \cdot 24$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{5} \cdot \frac{5 x}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 x}{4} = \frac{4}{5} \cdot 24$

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{4}{5} \cdot 24$

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{4}{5} \cdot 24$

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{4}{5} \cdot 24$

Rewrite the expression.

$x = \frac{4}{5} \cdot 24$

Simplify the right side.

Multiply $\frac{4}{5} \cdot 24$ .

Combine $\frac{4}{5}$ and $24$ .

$x = \frac{4 \cdot 24}{5}$

Multiply $4$ by $24$ .

$x = \frac{96}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{96}{5}$

Decimal Form:

$x = 19.2$

Mixed Number Form:

$x = 19 \frac{1}{5}$

Solve for x 3/4x-8=x/3

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