Question

Solve and justify your answer using the properties of operations (i.e Distributive property, associative property, commutative property, identity property, substitution, ect…)
-9 + 6x = -3(3 - 2x)

Answer 1

To solve the equation -9 + 6x = -3(3 - 2x), we will use the properties of operations to simplify and isolate the variable x.

First, let's distribute -3 to the terms inside the parentheses on the right-hand side of the equation:
-3(3 - 2x) = -9 + 6x

The equation now becomes -9 + 6x = -9 + 6x. We have a special case where both sides of the equation contain the same expression.

To further simplify this equation, we can add 9 to both sides:
-9 + 6x + 9 = -9 + 6x + 9
6x = 6x

The equation now becomes 6x = 6x. We haven't solved for x yet, but we have an equation where both sides are equal.

Now let's subtract 6x from both sides:
6x - 6x = 6x - 6x
0 = 0

The equation becomes 0 = 0. This equation is true for all real numbers. It means that any value of x will satisfy the equation.

Therefore, the solution to the equation -9 + 6x = -3(3 - 2x) is x belongs to the set of real numbers.