Solve for x 3(x-2)+4(2x-6)=6(x-4)+8(2x+1)

$3 (x - 2) + 4 (2 x - 6) = 6 (x - 4) + 8 (2 x + 1)$

Step 1

Simplify $3 (x - 2) + 4 (2 x - 6)$ .

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot - 2 + 4 (2 x - 6) = 6 (x - 4) + 8 (2 x + 1)$

Multiply $3$ by $- 2$ .

$3 x - 6 + 4 (2 x - 6) = 6 (x - 4) + 8 (2 x + 1)$

Apply the distributive property.

$3 x - 6 + 4 (2 x) + 4 \cdot - 6 = 6 (x - 4) + 8 (2 x + 1)$

Multiply $2$ by $4$ .

$3 x - 6 + 8 x + 4 \cdot - 6 = 6 (x - 4) + 8 (2 x + 1)$

Multiply $4$ by $- 6$ .

$3 x - 6 + 8 x - 24 = 6 (x - 4) + 8 (2 x + 1)$

Simplify by adding terms.

Add $3 x$ and $8 x$ .

$11 x - 6 - 24 = 6 (x - 4) + 8 (2 x + 1)$

Subtract $24$ from $- 6$ .

$11 x - 30 = 6 (x - 4) + 8 (2 x + 1)$

Step 2

Simplify $6 (x - 4) + 8 (2 x + 1)$ .

Simplify each term.

Apply the distributive property.

$11 x - 30 = 6 x + 6 \cdot - 4 + 8 (2 x + 1)$

Multiply $6$ by $- 4$ .

$11 x - 30 = 6 x - 24 + 8 (2 x + 1)$

Apply the distributive property.

$11 x - 30 = 6 x - 24 + 8 (2 x) + 8 \cdot 1$

Multiply $2$ by $8$ .

$11 x - 30 = 6 x - 24 + 16 x + 8 \cdot 1$

Multiply $8$ by $1$ .

$11 x - 30 = 6 x - 24 + 16 x + 8$

Simplify by adding terms.

Add $6 x$ and $16 x$ .

$11 x - 30 = 22 x - 24 + 8$

Add $- 24$ and $8$ .

$11 x - 30 = 22 x - 16$

Step 3

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

Subtract $22 x$ from both sides of the equation.

$11 x - 30 - 22 x = - 16$

Subtract $22 x$ from $11 x$ .

$- 11 x - 30 = - 16$

Step 4

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

Add $30$ to both sides of the equation.

$- 11 x = - 16 + 30$

Add $- 16$ and $30$ .

$- 11 x = 14$

Step 5

Divide each term in $- 11 x = 14$ by $- 11$ and simplify.

Divide each term in $- 11 x = 14$ by $- 11$ .

$\frac{- 11 x}{- 11} = \frac{14}{- 11}$

Simplify the left side.

Cancel the common factor of $- 11$ .

Cancel the common factor.

$\frac{- 11 x}{- 11} = \frac{14}{- 11}$

Divide $x$ by $1$ .

$x = \frac{14}{- 11}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{14}{11}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{14}{11}$

Decimal Form:

$x = - 1.\overline{27}$

Mixed Number Form:

$x = - 1 \frac{3}{11}$

Solve for x 3(x-2)+4(2x-6)=6(x-4)+8(2x+1)

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