Is 2 (x - 1) + 18 equivalent to 6 (x + 3) - 4x - 6? Use algebra to find your answer. Show your work.

Answer 1

To determine if 2(x - 1) + 18 is equivalent to 6(x + 3) - 4x - 6, we will simplify both expressions and compare them.

First, let's simplify the expression 2(x - 1) + 18:

2(x - 1) + 18
= 2x - 2 + 18 (Distributive property)
= 2x + 16 (Combine like terms)

Now let's simplify the expression 6(x + 3) - 4x - 6:

6(x + 3) - 4x - 6
= 6x + 18 - 4x - 6 (Distributive property)
= 2x + 12 (Combine like terms)

Now we can compare the simplified expressions:

2x + 16 = 2x + 12

Since the left side is equal to the right side, we can conclude that 2(x - 1) + 18 is equivalent to 6(x + 3) - 4x - 6.