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

$2 + 5 (x + 3) - 3 (x - 4) = x + 2 (2 x + 4)$

Step 1

Simplify $2 + 5 (x + 3) - 3 (x - 4)$ .

Simplify each term.

Apply the distributive property.

$2 + 5 x + 5 \cdot 3 - 3 (x - 4) = x + 2 (2 x + 4)$

Multiply $5$ by $3$ .

$2 + 5 x + 15 - 3 (x - 4) = x + 2 (2 x + 4)$

Apply the distributive property.

$2 + 5 x + 15 - 3 x - 3 \cdot - 4 = x + 2 (2 x + 4)$

Multiply $- 3$ by $- 4$ .

$2 + 5 x + 15 - 3 x + 12 = x + 2 (2 x + 4)$

Simplify by adding terms.

Add $2$ and $15$ .

$5 x + 17 - 3 x + 12 = x + 2 (2 x + 4)$

Subtract $3 x$ from $5 x$ .

$2 x + 17 + 12 = x + 2 (2 x + 4)$

Add $17$ and $12$ .

$2 x + 29 = x + 2 (2 x + 4)$

Step 2

Simplify $x + 2 (2 x + 4)$ .

Simplify each term.

Apply the distributive property.

$2 x + 29 = x + 2 (2 x) + 2 \cdot 4$

Multiply $2$ by $2$ .

$2 x + 29 = x + 4 x + 2 \cdot 4$

Multiply $2$ by $4$ .

$2 x + 29 = x + 4 x + 8$

Add $x$ and $4 x$ .

$2 x + 29 = 5 x + 8$

Step 3

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

Subtract $5 x$ from both sides of the equation.

$2 x + 29 - 5 x = 8$

Subtract $5 x$ from $2 x$ .

$- 3 x + 29 = 8$

Step 4

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

Subtract $29$ from both sides of the equation.

$- 3 x = 8 - 29$

Subtract $29$ from $8$ .

$- 3 x = - 21$

Step 5

Divide each term in $- 3 x = - 21$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 21$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 21}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 21}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 21}{- 3}$

Simplify the right side.

Divide $- 21$ by $- 3$ .

$x = 7$

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

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