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

[AI-generated answer — Bot GPT 3.5]

To solve the equation -9 + 6x = -3(3 - 2x), we will simplify the expressions on both sides of the equation using the properties of operations.

Starting with the left side of the equation, we have -9 + 6x. Since there is no other term containing a constant (-9), we can leave it as it is.

For the right side of the equation, we have -3(3 - 2x). We need to distribute the -3 to both terms inside the parentheses.

-3(3) = -9
-3(-2x) = 6x

Now the equation becomes:

-9 + 6x = -9 + 6x

Next, we can use the commutative property to rearrange the terms on both sides of the equation:

-9 + 6x = 6x - 9

We notice that the equation now has the same terms on both sides in a different order. This suggests that the equation will likely have infinitely many solutions.

To confirm this, we subtract 6x from both sides of the equation:

-9 + 6x - 6x = 6x - 9 - 6x
-9 = -9

The equation simplifies to -9 = -9, which is a true statement. This means that the equation -9 + 6x = -3(3 - 2x) is true for all real values of x.

Thus, the solution to the equation is x belongs to the set of real numbers, denoted as x ∈ ℝ.