Solve and justify your answer using the properties of operations (i.e Distributive property, associative property, commutative property, identity property, substitution, ect…)

Question

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

Answer 1

To solve the equation -9 + 6x = -3(3 - 2x), we can start by simplifying both sides of the equation.

First, we can simplify the right side of the equation: -3(3 - 2x) using the distributive property.

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

So the equation -9 + 6x = -3(3 - 2x) simplifies to -9 + 6x = -9 + 6x.

Next, we can manipulate the equation to isolate the variable x.

Adding 9 to both sides of the equation gives:
-9 + 9 + 6x = -9 + 6x + 9
0 + 6x = 0 + 6x

The equation simplifies to 6x = 6x.

At this point, we can use the commutative property of addition to rearrange the terms on the left side of the equation:
6x = x * 6

Next, we can use the division property of equality to divide both sides of the equation by 6:
(6x)/6 = (x * 6)/6
x = 1 * x

Finally, using the identity property of multiplication and the substitution property of equality, we can conclude that:
x = x

Therefore, the solution to the equation -9 + 6x = -3(3 - 2x) is x = x, indicating that x could be any real number.