Solve for x 7(x-2)+3(x+2)=5(x-6)

$7 (x - 2) + 3 (x + 2) = 5 (x - 6)$

Step 1

Simplify $7 (x - 2) + 3 (x + 2)$ .

Simplify each term.

Apply the distributive property.

$7 x + 7 \cdot - 2 + 3 (x + 2) = 5 (x - 6)$

Multiply $7$ by $- 2$ .

$7 x - 14 + 3 (x + 2) = 5 (x - 6)$

Apply the distributive property.

$7 x - 14 + 3 x + 3 \cdot 2 = 5 (x - 6)$

Multiply $3$ by $2$ .

$7 x - 14 + 3 x + 6 = 5 (x - 6)$

Simplify by adding terms.

Add $7 x$ and $3 x$ .

$10 x - 14 + 6 = 5 (x - 6)$

Add $- 14$ and $6$ .

$10 x - 8 = 5 (x - 6)$

Step 2

Simplify $5 (x - 6)$ .

Apply the distributive property.

$10 x - 8 = 5 x + 5 \cdot - 6$

Multiply $5$ by $- 6$ .

$10 x - 8 = 5 x - 30$

Step 3

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

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

$10 x - 8 - 5 x = - 30$

Subtract $5 x$ from $10 x$ .

$5 x - 8 = - 30$

Step 4

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

Add $8$ to both sides of the equation.

$5 x = - 30 + 8$

Add $- 30$ and $8$ .

$5 x = - 22$

Step 5

Divide each term in $5 x = - 22$ by $5$ and simplify.

Divide each term in $5 x = - 22$ by $5$ .

$\frac{5 x}{5} = \frac{- 22}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 22}{5}$

Divide $x$ by $1$ .

$x = \frac{- 22}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{22}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{22}{5}$

Decimal Form:

$x = - 4.4$

Mixed Number Form:

$x = - 4 \frac{2}{5}$

Solve for x 7(x-2)+3(x+2)=5(x-6)

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