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

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

Step 1

Simplify $4 (2 x - 3) + 8 (x - 4)$ .

Simplify each term.

Apply the distributive property.

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

Multiply $2$ by $4$ .

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

Multiply $4$ by $- 3$ .

$8 x - 12 + 8 (x - 4) = 2 (2 x + 6)$

Apply the distributive property.

$8 x - 12 + 8 x + 8 \cdot - 4 = 2 (2 x + 6)$

Multiply $8$ by $- 4$ .

$8 x - 12 + 8 x - 32 = 2 (2 x + 6)$

Simplify by adding terms.

Add $8 x$ and $8 x$ .

$16 x - 12 - 32 = 2 (2 x + 6)$

Subtract $32$ from $- 12$ .

$16 x - 44 = 2 (2 x + 6)$

Step 2

Simplify $2 (2 x + 6)$ .

Apply the distributive property.

$16 x - 44 = 2 (2 x) + 2 \cdot 6$

Multiply.

Multiply $2$ by $2$ .

$16 x - 44 = 4 x + 2 \cdot 6$

Multiply $2$ by $6$ .

$16 x - 44 = 4 x + 12$

Step 3

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

Subtract $4 x$ from both sides of the equation.

$16 x - 44 - 4 x = 12$

Subtract $4 x$ from $16 x$ .

$12 x - 44 = 12$

Step 4

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

Add $44$ to both sides of the equation.

$12 x = 12 + 44$

Add $12$ and $44$ .

$12 x = 56$

Step 5

Divide each term in $12 x = 56$ by $12$ and simplify.

Divide each term in $12 x = 56$ by $12$ .

$\frac{12 x}{12} = \frac{56}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} = \frac{56}{12}$

Divide $x$ by $1$ .

$x = \frac{56}{12}$

Simplify the right side.

Cancel the common factor of $56$ and $12$ .

Factor $4$ out of $56$ .

$x = \frac{4 (14)}{12}$

Cancel the common factors.

Factor $4$ out of $12$ .

$x = \frac{4 \cdot 14}{4 \cdot 3}$

Cancel the common factor.

$x = \frac{4 \cdot 14}{4 \cdot 3}$

Rewrite the expression.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 4.\overline{6}$

Mixed Number Form:

$x = 4 \frac{2}{3}$

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

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