Solve for x (3x)/2=1+(4x)/3

$\frac{3 x}{2} = 1 + \frac{4 x}{3}$

Step 1

Multiply both sides by $2$ .

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

Step 2

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Simplify $(1 + \frac{4 x}{3}) \cdot 2$ .

Apply the distributive property.

$3 x = 1 \cdot 2 + \frac{4 x}{3} \cdot 2$

Multiply $2$ by $1$ .

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

Multiply $\frac{4 x}{3} \cdot 2$ .

Combine $\frac{4 x}{3}$ and $2$ .

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

Multiply $2$ by $4$ .

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

Reorder $2$ and $\frac{8 x}{3}$ .

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

Step 3

Solve for $x$ .

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

Subtract $\frac{8 x}{3}$ from both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Factor $x$ out of $3 x \cdot 3 - 8 x$ .

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

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

Factor $x$ out of $- 8 x$ .

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

Factor $x$ out of $x (3 \cdot 3) + x \cdot - 8$ .

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

Multiply $3$ by $3$ .

$\frac{x (9 - 8)}{3} = 2$

Subtract $8$ from $9$ .

$\frac{x \cdot 1}{3} = 2$

Multiply $x$ by $1$ .

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

Multiply both sides of the equation by $3$ .

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

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$x = 3 \cdot 2$

Simplify the right side.

Multiply $3$ by $2$ .

$x = 6$

Solve for x (3x)/2=1+(4x)/3

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