Solve for x x(8+2)+3=2(5+x)+5(x+1)-6

$x (8 + 2) + 3 = 2 (5 + x) + 5 (x + 1) - 6$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$2 (5 + x) + 5 (x + 1) - 6 = x (8 + 2) + 3$

Step 2

Simplify $2 (5 + x) + 5 (x + 1) - 6$ .

Simplify each term.

Apply the distributive property.

$2 \cdot 5 + 2 x + 5 (x + 1) - 6 = x (8 + 2) + 3$

Multiply $2$ by $5$ .

$10 + 2 x + 5 (x + 1) - 6 = x (8 + 2) + 3$

Apply the distributive property.

$10 + 2 x + 5 x + 5 \cdot 1 - 6 = x (8 + 2) + 3$

Multiply $5$ by $1$ .

$10 + 2 x + 5 x + 5 - 6 = x (8 + 2) + 3$

Simplify by adding terms.

Add $10$ and $5$ .

$2 x + 5 x + 15 - 6 = x (8 + 2) + 3$

Add $2 x$ and $5 x$ .

$7 x + 15 - 6 = x (8 + 2) + 3$

Subtract $6$ from $15$ .

$7 x + 9 = x (8 + 2) + 3$

Step 3

Simplify each term.

Add $8$ and $2$ .

$7 x + 9 = x \cdot 10 + 3$

Move $10$ to the left of $x$ .

$7 x + 9 = 10 x + 3$

Step 4

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

Subtract $10 x$ from both sides of the equation.

$7 x + 9 - 10 x = 3$

Subtract $10 x$ from $7 x$ .

$- 3 x + 9 = 3$

Step 5

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

Subtract $9$ from both sides of the equation.

$- 3 x = 3 - 9$

Subtract $9$ from $3$ .

$- 3 x = - 6$

Step 6

Divide each term in $- 3 x = - 6$ by $- 3$ and simplify.

Divide each term in $- 3 x = - 6$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{- 6}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{- 6}{- 3}$

Divide $x$ by $1$ .

$x = \frac{- 6}{- 3}$

Simplify the right side.

Divide $- 6$ by $- 3$ .

$x = 2$

Solve for x x(8+2)+3=2(5+x)+5(x+1)-6

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