Solve for x 8(x+1)-3(x+4)=7(2-x)

$8 (x + 1) - 3 (x + 4) = 7 (2 - x)$

Step 1

Simplify $8 (x + 1) - 3 (x + 4)$ .

Simplify each term.

Apply the distributive property.

$8 x + 8 \cdot 1 - 3 (x + 4) = 7 (2 - x)$

Multiply $8$ by $1$ .

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

Apply the distributive property.

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

Multiply $- 3$ by $4$ .

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

Simplify by adding terms.

Subtract $3 x$ from $8 x$ .

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

Subtract $12$ from $8$ .

$5 x - 4 = 7 (2 - x)$

Step 2

Simplify $7 (2 - x)$ .

Apply the distributive property.

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

Multiply.

Multiply $7$ by $2$ .

$5 x - 4 = 14 + 7 (- x)$

Multiply $- 1$ by $7$ .

$5 x - 4 = 14 - 7 x$

Step 3

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

Add $7 x$ to both sides of the equation.

$5 x - 4 + 7 x = 14$

Add $5 x$ and $7 x$ .

$12 x - 4 = 14$

Step 4

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

Add $4$ to both sides of the equation.

$12 x = 14 + 4$

Add $14$ and $4$ .

$12 x = 18$

Step 5

Divide each term in $12 x = 18$ by $12$ and simplify.

Divide each term in $12 x = 18$ by $12$ .

$\frac{12 x}{12} = \frac{18}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 x}{12} = \frac{18}{12}$

Divide $x$ by $1$ .

$x = \frac{18}{12}$

Simplify the right side.

Cancel the common factor of $18$ and $12$ .

Factor $6$ out of $18$ .

$x = \frac{6 (3)}{12}$

Cancel the common factors.

Factor $6$ out of $12$ .

$x = \frac{6 \cdot 3}{6 \cdot 2}$

Cancel the common factor.

$x = \frac{6 \cdot 3}{6 \cdot 2}$

Rewrite the expression.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.5$

Mixed Number Form:

$x = 1 \frac{1}{2}$

Solve for x 8(x+1)-3(x+4)=7(2-x)

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