Solve for x (3x)/4+(2x)/3=51

$\frac{3 x}{4} + \frac{2 x}{3} = 51$

Step 1

Simplify $\frac{3 x}{4} + \frac{2 x}{3}$ .

To write $\frac{3 x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 x}{4} \cdot \frac{3}{3} + \frac{2 x}{3} = 51$

To write $\frac{2 x}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 x}{4} \cdot \frac{3}{3} + \frac{2 x}{3} \cdot \frac{4}{4} = 51$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{3 x \cdot 3}{4 \cdot 3} + \frac{2 x}{3} \cdot \frac{4}{4} = 51$

Multiply $4$ by $3$ .

$\frac{3 x \cdot 3}{12} + \frac{2 x}{3} \cdot \frac{4}{4} = 51$

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

$\frac{3 x \cdot 3}{12} + \frac{2 x \cdot 4}{3 \cdot 4} = 51$

Multiply $3$ by $4$ .

$\frac{3 x \cdot 3}{12} + \frac{2 x \cdot 4}{12} = 51$

Combine the numerators over the common denominator.

$\frac{3 x \cdot 3 + 2 x \cdot 4}{12} = 51$

Simplify the numerator.

Factor $x$ out of $3 x \cdot 3 + 2 x \cdot 4$ .

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

$\frac{x (3 \cdot 3) + 2 x \cdot 4}{12} = 51$

Factor $x$ out of $2 x \cdot 4$ .

$\frac{x (3 \cdot 3) + x (2 \cdot 4)}{12} = 51$

Factor $x$ out of $x (3 \cdot 3) + x (2 \cdot 4)$ .

$\frac{x (3 \cdot 3 + 2 \cdot 4)}{12} = 51$

Multiply $3$ by $3$ .

$\frac{x (9 + 2 \cdot 4)}{12} = 51$

Multiply $2$ by $4$ .

$\frac{x (9 + 8)}{12} = 51$

Add $9$ and $8$ .

$\frac{x \cdot 17}{12} = 51$

Move $17$ to the left of $x$ .

$\frac{17 x}{12} = 51$

Step 2

Multiply both sides of the equation by $\frac{12}{17}$ .

$\frac{12}{17} \cdot \frac{17 x}{12} = \frac{12}{17} \cdot 51$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{12}{17} \cdot \frac{17 x}{12}$ .

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12}{17} \cdot \frac{17 x}{12} = \frac{12}{17} \cdot 51$

Rewrite the expression.

$\frac{1}{17} (17 x) = \frac{12}{17} \cdot 51$

Cancel the common factor of $17$ .

Factor $17$ out of $17 x$ .

$\frac{1}{17} (17 (x)) = \frac{12}{17} \cdot 51$

Cancel the common factor.

$\frac{1}{17} (17 x) = \frac{12}{17} \cdot 51$

Rewrite the expression.

$x = \frac{12}{17} \cdot 51$

Simplify the right side.

Simplify $\frac{12}{17} \cdot 51$ .

Cancel the common factor of $17$ .

Factor $17$ out of $51$ .

$x = \frac{12}{17} \cdot (17 (3))$

Cancel the common factor.

$x = \frac{12}{17} \cdot (17 \cdot 3)$

Rewrite the expression.

$x = 12 \cdot 3$

Multiply $12$ by $3$ .

$x = 36$

Solve for x (3x)/4+(2x)/3=51

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