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

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

Step 1

Multiply both sides by $13$ .

$\frac{3 (2 x + 3)}{13} \cdot 13 = (2 x - 7) \cdot 13$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{3 (2 x + 3)}{13} \cdot 13$ .

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{3 (2 x + 3)}{13} \cdot 13 = (2 x - 7) \cdot 13$

Rewrite the expression.

$3 (2 x + 3) = (2 x - 7) \cdot 13$

Apply the distributive property.

$3 (2 x) + 3 \cdot 3 = (2 x - 7) \cdot 13$

Multiply.

Multiply $2$ by $3$ .

$6 x + 3 \cdot 3 = (2 x - 7) \cdot 13$

Multiply $3$ by $3$ .

$6 x + 9 = (2 x - 7) \cdot 13$

Simplify the right side.

Simplify $(2 x - 7) \cdot 13$ .

Apply the distributive property.

$6 x + 9 = 2 x \cdot 13 - 7 \cdot 13$

Multiply.

Multiply $13$ by $2$ .

$6 x + 9 = 26 x - 7 \cdot 13$

Multiply $- 7$ by $13$ .

$6 x + 9 = 26 x - 91$

Step 3

Solve for $x$ .

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

Subtract $26 x$ from both sides of the equation.

$6 x + 9 - 26 x = - 91$

Subtract $26 x$ from $6 x$ .

$- 20 x + 9 = - 91$

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

Subtract $9$ from both sides of the equation.

$- 20 x = - 91 - 9$

Subtract $9$ from $- 91$ .

$- 20 x = - 100$

Divide each term in $- 20 x = - 100$ by $- 20$ and simplify.

Divide each term in $- 20 x = - 100$ by $- 20$ .

$\frac{- 20 x}{- 20} = \frac{- 100}{- 20}$

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

$\frac{- 20 x}{- 20} = \frac{- 100}{- 20}$

Divide $x$ by $1$ .

$x = \frac{- 100}{- 20}$

Simplify the right side.

Divide $- 100$ by $- 20$ .

$x = 5$

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

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