Solve for x 12(2x-8)=4(5-2x)+3(7-3x)

$12 (2 x - 8) = 4 (5 - 2 x) + 3 (7 - 3 x)$

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.

$4 (5 - 2 x) + 3 (7 - 3 x) = 12 (2 x - 8)$

Step 2

Simplify $4 (5 - 2 x) + 3 (7 - 3 x)$ .

Simplify each term.

Apply the distributive property.

$4 \cdot 5 + 4 (- 2 x) + 3 (7 - 3 x) = 12 (2 x - 8)$

Multiply $4$ by $5$ .

$20 + 4 (- 2 x) + 3 (7 - 3 x) = 12 (2 x - 8)$

Multiply $- 2$ by $4$ .

$20 - 8 x + 3 (7 - 3 x) = 12 (2 x - 8)$

Apply the distributive property.

$20 - 8 x + 3 \cdot 7 + 3 (- 3 x) = 12 (2 x - 8)$

Multiply $3$ by $7$ .

$20 - 8 x + 21 + 3 (- 3 x) = 12 (2 x - 8)$

Multiply $- 3$ by $3$ .

$20 - 8 x + 21 - 9 x = 12 (2 x - 8)$

Simplify by adding terms.

Add $20$ and $21$ .

$- 8 x + 41 - 9 x = 12 (2 x - 8)$

Subtract $9 x$ from $- 8 x$ .

$- 17 x + 41 = 12 (2 x - 8)$

Step 3

Simplify $12 (2 x - 8)$ .

Apply the distributive property.

$- 17 x + 41 = 12 (2 x) + 12 \cdot - 8$

Multiply.

Multiply $2$ by $12$ .

$- 17 x + 41 = 24 x + 12 \cdot - 8$

Multiply $12$ by $- 8$ .

$- 17 x + 41 = 24 x - 96$

Step 4

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

Subtract $24 x$ from both sides of the equation.

$- 17 x + 41 - 24 x = - 96$

Subtract $24 x$ from $- 17 x$ .

$- 41 x + 41 = - 96$

Step 5

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

Subtract $41$ from both sides of the equation.

$- 41 x = - 96 - 41$

Subtract $41$ from $- 96$ .

$- 41 x = - 137$

Step 6

Divide each term in $- 41 x = - 137$ by $- 41$ and simplify.

Divide each term in $- 41 x = - 137$ by $- 41$ .

$\frac{- 41 x}{- 41} = \frac{- 137}{- 41}$

Simplify the left side.

Cancel the common factor of $- 41$ .

Cancel the common factor.

$\frac{- 41 x}{- 41} = \frac{- 137}{- 41}$

Divide $x$ by $1$ .

$x = \frac{- 137}{- 41}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{137}{41}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \frac{137}{41}$

Decimal Form:

$x = 3.\overline{34146}$

Mixed Number Form:

$x = 3 \frac{14}{41}$

Solve for x 12(2x-8)=4(5-2x)+3(7-3x)

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