Solve for x 6(x-4)+6=4x+2(x-9)

$6 (x - 4) + 6 = 4 x + 2 (x - 9)$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$4 x + 2 (x - 9) = 6 (x - 4) + 6$

Step 2

Simplify $4 x + 2 (x - 9)$ .

Simplify each term.

Apply the distributive property.

$4 x + 2 x + 2 \cdot - 9 = 6 (x - 4) + 6$

Multiply $2$ by $- 9$ .

$4 x + 2 x - 18 = 6 (x - 4) + 6$

Add $4 x$ and $2 x$ .

$6 x - 18 = 6 (x - 4) + 6$

Step 3

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

Simplify each term.

Apply the distributive property.

$6 x - 18 = 6 x + 6 \cdot - 4 + 6$

Multiply $6$ by $- 4$ .

$6 x - 18 = 6 x - 24 + 6$

Add $- 24$ and $6$ .

$6 x - 18 = 6 x - 18$

Step 4

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

Subtract $6 x$ from both sides of the equation.

$6 x - 18 - 6 x = - 18$

Combine the opposite terms in $6 x - 18 - 6 x$ .

Subtract $6 x$ from $6 x$ .

$0 - 18 = - 18$

Subtract $18$ from $0$ .

$- 18 = - 18$

Step 5

Since $- 18 = - 18$ , the equation will always be true for any value of $x$ .

All real numbers

Step 6

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$