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

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

Step 1

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

Simplify each term.

Apply the distributive property.

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

Multiply $7$ by $- 3$ .

$7 x - 21 + 3 (4 - x) = - 8$

Apply the distributive property.

$7 x - 21 + 3 \cdot 4 + 3 (- x) = - 8$

Multiply $3$ by $4$ .

$7 x - 21 + 12 + 3 (- x) = - 8$

Multiply $- 1$ by $3$ .

$7 x - 21 + 12 - 3 x = - 8$

Simplify by adding terms.

Subtract $3 x$ from $7 x$ .

$4 x - 21 + 12 = - 8$

Add $- 21$ and $12$ .

$4 x - 9 = - 8$

Step 2

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

Add $9$ to both sides of the equation.

$4 x = - 8 + 9$

Add $- 8$ and $9$ .

$4 x = 1$

Step 3

Divide each term in $4 x = 1$ by $4$ and simplify.

Divide each term in $4 x = 1$ by $4$ .

$\frac{4 x}{4} = \frac{1}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{1}{4}$

Divide $x$ by $1$ .

$x = \frac{1}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{4}$

Decimal Form:

$x = 0.25$