Find All Complex Solutions 3x-7=3(x-3)+2

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

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

Simplify each term.

Apply the distributive property.

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

Multiply $3$ by $- 3$ .

$3 x - 7 = 3 x - 9 + 2$

Add $- 9$ and $2$ .

$3 x - 7 = 3 x - 7$

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

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

$3 x - 7 - 3 x = - 7$

Combine the opposite terms in $3 x - 7 - 3 x$ .

Subtract $3 x$ from $3 x$ .

$0 - 7 = - 7$

Subtract $7$ from $0$ .

$- 7 = - 7$

Since $- 7 = - 7$ , the equation will always be true.

Always true