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

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

Step 1

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

Simplify each term.

Apply the distributive property.

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

Multiply $4$ by $3$ .

$12 + 4 x - x = 6 + 3 (x + 2)$

Subtract $x$ from $4 x$ .

$12 + 3 x = 6 + 3 (x + 2)$

Step 2

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

Simplify each term.

Apply the distributive property.

$12 + 3 x = 6 + 3 x + 3 \cdot 2$

Multiply $3$ by $2$ .

$12 + 3 x = 6 + 3 x + 6$

Add $6$ and $6$ .

$12 + 3 x = 3 x + 12$

Step 3

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

Subtract $3 x$ from both sides of the equation.

$12 + 3 x - 3 x = 12$

Combine the opposite terms in $12 + 3 x - 3 x$ .

Subtract $3 x$ from $3 x$ .

$12 + 0 = 12$

Add $12$ and $0$ .

$12 = 12$

Step 4

Since $12 = 12$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$