Solve for x 6(x-4)+x=5(x-2)

$6 (x - 4) + x = 5 (x - 2)$

Step 1

Simplify $6 (x - 4) + x$ .

Simplify each term.

Apply the distributive property.

$6 x + 6 \cdot - 4 + x = 5 (x - 2)$

Multiply $6$ by $- 4$ .

$6 x - 24 + x = 5 (x - 2)$

Add $6 x$ and $x$ .

$7 x - 24 = 5 (x - 2)$

Step 2

Simplify $5 (x - 2)$ .

Apply the distributive property.

$7 x - 24 = 5 x + 5 \cdot - 2$

Multiply $5$ by $- 2$ .

$7 x - 24 = 5 x - 10$

Step 3

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

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

$7 x - 24 - 5 x = - 10$

Subtract $5 x$ from $7 x$ .

$2 x - 24 = - 10$

Step 4

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

Add $24$ to both sides of the equation.

$2 x = - 10 + 24$

Add $- 10$ and $24$ .

$2 x = 14$

Step 5

Divide each term in $2 x = 14$ by $2$ and simplify.

Divide each term in $2 x = 14$ by $2$ .

$\frac{2 x}{2} = \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{14}{2}$

Divide $x$ by $1$ .

$x = \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$x = 7$