Solve for x 3(3x+2)-2x=7x+6

$3 (3 x + 2) - 2 x = 7 x + 6$

Step 1

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

Simplify each term.

Apply the distributive property.

$3 (3 x) + 3 \cdot 2 - 2 x = 7 x + 6$

Multiply $3$ by $3$ .

$9 x + 3 \cdot 2 - 2 x = 7 x + 6$

Multiply $3$ by $2$ .

$9 x + 6 - 2 x = 7 x + 6$

Subtract $2 x$ from $9 x$ .

$7 x + 6 = 7 x + 6$

Step 2

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

Subtract $7 x$ from both sides of the equation.

$7 x + 6 - 7 x = 6$

Combine the opposite terms in $7 x + 6 - 7 x$ .

Subtract $7 x$ from $7 x$ .

$0 + 6 = 6$

Add $0$ and $6$ .

$6 = 6$

Step 3

Since $6 = 6$ , the equation will always be true for any value of $x$ .

All real numbers

Step 4

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$