Solve for x (3x+5)/4-(2x-1)/3=2

$\frac{3 x + 5}{4} - \frac{2 x - 1}{3} = 2$

Simplify $\frac{3 x + 5}{4} - \frac{2 x - 1}{3}$ .

To write $\frac{3 x + 5}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 x + 5}{4} \cdot \frac{3}{3} - \frac{2 x - 1}{3} = 2$

To write $- \frac{2 x - 1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 x + 5}{4} \cdot \frac{3}{3} - \frac{2 x - 1}{3} \cdot \frac{4}{4} = 2$

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

Multiply $\frac{3 x + 5}{4}$ by $\frac{3}{3}$ .

$\frac{(3 x + 5) \cdot 3}{4 \cdot 3} - \frac{2 x - 1}{3} \cdot \frac{4}{4} = 2$

Multiply $4$ by $3$ .

$\frac{(3 x + 5) \cdot 3}{12} - \frac{2 x - 1}{3} \cdot \frac{4}{4} = 2$

Multiply $\frac{2 x - 1}{3}$ by $\frac{4}{4}$ .

$\frac{(3 x + 5) \cdot 3}{12} - \frac{(2 x - 1) \cdot 4}{3 \cdot 4} = 2$

Multiply $3$ by $4$ .

$\frac{(3 x + 5) \cdot 3}{12} - \frac{(2 x - 1) \cdot 4}{12} = 2$

Combine the numerators over the common denominator.

$\frac{(3 x + 5) \cdot 3 - (2 x - 1) \cdot 4}{12} = 2$

Simplify the numerator.

Apply the distributive property.

$\frac{3 x \cdot 3 + 5 \cdot 3 - (2 x - 1) \cdot 4}{12} = 2$

Multiply $3$ by $3$ .

$\frac{9 x + 5 \cdot 3 - (2 x - 1) \cdot 4}{12} = 2$

Multiply $5$ by $3$ .

$\frac{9 x + 15 - (2 x - 1) \cdot 4}{12} = 2$

Apply the distributive property.

$\frac{9 x + 15 + (- (2 x) - - 1) \cdot 4}{12} = 2$

Multiply $2$ by $- 1$ .

$\frac{9 x + 15 + (- 2 x - - 1) \cdot 4}{12} = 2$

Multiply $- 1$ by $- 1$ .

$\frac{9 x + 15 + (- 2 x + 1) \cdot 4}{12} = 2$

Apply the distributive property.

$\frac{9 x + 15 - 2 x \cdot 4 + 1 \cdot 4}{12} = 2$

Multiply $4$ by $- 2$ .

$\frac{9 x + 15 - 8 x + 1 \cdot 4}{12} = 2$

Multiply $4$ by $1$ .

$\frac{9 x + 15 - 8 x + 4}{12} = 2$

Subtract $8 x$ from $9 x$ .

$\frac{x + 15 + 4}{12} = 2$

Add $15$ and $4$ .

$\frac{x + 19}{12} = 2$

Multiply both sides of the equation by $12$ .

$12 \frac{x + 19}{12} = 12 \cdot 2$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$12 \frac{x + 19}{12} = 12 \cdot 2$

Rewrite the expression.

$x + 19 = 12 \cdot 2$

Simplify the right side.

Multiply $12$ by $2$ .

$x + 19 = 24$

Move all terms not containing $x$ to the right side of the equation.

Subtract $19$ from both sides of the equation.

$x = 24 - 19$

Subtract $19$ from $24$ .

$x = 5$

Solve for x (3x+5)/4-(2x-1)/3=2

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