Solve for x x/3+x/2=10

$\frac{x}{3} + \frac{x}{2} = 10$

Step 1

Simplify $\frac{x}{3} + \frac{x}{2}$ .

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{3} \cdot \frac{2}{2} + \frac{x}{2} = 10$

To write $\frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{3} \cdot \frac{2}{2} + \frac{x}{2} \cdot \frac{3}{3} = 10$

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{3}$ by $\frac{2}{2}$ .

$\frac{x \cdot 2}{3 \cdot 2} + \frac{x}{2} \cdot \frac{3}{3} = 10$

Multiply $3$ by $2$ .

$\frac{x \cdot 2}{6} + \frac{x}{2} \cdot \frac{3}{3} = 10$

Multiply $\frac{x}{2}$ by $\frac{3}{3}$ .

$\frac{x \cdot 2}{6} + \frac{x \cdot 3}{2 \cdot 3} = 10$

Multiply $2$ by $3$ .

$\frac{x \cdot 2}{6} + \frac{x \cdot 3}{6} = 10$

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + x \cdot 3}{6} = 10$

Simplify the numerator.

Move $2$ to the left of $x$ .

$\frac{2 \cdot x + x \cdot 3}{6} = 10$

Move $3$ to the left of $x$ .

$\frac{2 x + 3 \cdot x}{6} = 10$

Add $2 x$ and $3 x$ .

$\frac{5 x}{6} = 10$

Step 2

Multiply both sides of the equation by $\frac{6}{5}$ .

$\frac{6}{5} \cdot \frac{5 x}{6} = \frac{6}{5} \cdot 10$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{6}{5} \cdot \frac{5 x}{6}$ .

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6}{5} \cdot \frac{5 x}{6} = \frac{6}{5} \cdot 10$

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{6}{5} \cdot 10$

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{6}{5} \cdot 10$

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{6}{5} \cdot 10$

Rewrite the expression.

$x = \frac{6}{5} \cdot 10$

Simplify the right side.

Simplify $\frac{6}{5} \cdot 10$ .

Cancel the common factor of $5$ .

Factor $5$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

$x = 6 \cdot 2$

Multiply $6$ by $2$ .

$x = 12$

Solve for x x/3+x/2=10

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