Solve for x (3(7x+13))/(12x+15)=2

$\frac{3 (7 x + 13)}{12 x + 15} = 2$

Step 1

Factor each term.

Factor $3$ out of $12 x + 15$ .

Factor $3$ out of $12 x$ .

$\frac{3 (7 x + 13)}{3 (4 x) + 15} = 2$

Factor $3$ out of $15$ .

$\frac{3 (7 x + 13)}{3 (4 x) + 3 (5)} = 2$

Factor $3$ out of $3 (4 x) + 3 (5)$ .

$\frac{3 (7 x + 13)}{3 (4 x + 5)} = 2$

Reduce the expression $\frac{3 (7 x + 13)}{3 (4 x + 5)}$ by cancelling the common factors.

Cancel the common factor.

$\frac{3 (7 x + 13)}{3 (4 x + 5)} = 2$

Rewrite the expression.

$\frac{7 x + 13}{4 x + 5} = 2$

Step 2

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$4 x + 5, 1$

Remove parentheses.

$4 x + 5, 1$

The LCM of one and any expression is the expression.

$4 x + 5$

Step 3

Multiply each term in $\frac{7 x + 13}{4 x + 5} = 2$ by $4 x + 5$ to eliminate the fractions.

Multiply each term in $\frac{7 x + 13}{4 x + 5} = 2$ by $4 x + 5$ .

$\frac{7 x + 13}{4 x + 5} (4 x + 5) = 2 (4 x + 5)$

Simplify the left side.

Cancel the common factor of $4 x + 5$ .

Cancel the common factor.

$\frac{7 x + 13}{4 x + 5} (4 x + 5) = 2 (4 x + 5)$

Rewrite the expression.

$7 x + 13 = 2 (4 x + 5)$

Simplify the right side.

Apply the distributive property.

$7 x + 13 = 2 (4 x) + 2 \cdot 5$

Multiply.

Multiply $4$ by $2$ .

$7 x + 13 = 8 x + 2 \cdot 5$

Multiply $2$ by $5$ .

$7 x + 13 = 8 x + 10$

Step 4

Solve the equation.

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

Subtract $8 x$ from both sides of the equation.

$7 x + 13 - 8 x = 10$

Subtract $8 x$ from $7 x$ .

$- x + 13 = 10$

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

Subtract $13$ from both sides of the equation.

$- x = 10 - 13$

Subtract $13$ from $10$ .

$- x = - 3$

Divide each term in $- x = - 3$ by $- 1$ and simplify.

Divide each term in $- x = - 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 3}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 3}{- 1}$

Simplify the right side.

Divide $- 3$ by $- 1$ .

$x = 3$

Solve for x (3(7x+13))/(12x+15)=2

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