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

Answer 1

To determine if the two expressions are equivalent, we can simplify each expression and check if the results are the same.

Let's first simplify the expression 2(x−1)+18:
2(x−1) can be expanded using the distributive property:
2x − 2.

So, the simplified expression is:
2(x−1) + 18 = 2x − 2 + 18 = 2x + 16.

Now, let's simplify the expression 6(x+3)−4x−6:
6(x+3) can be expanded using the distributive property:
6x + 18.

So, the simplified expression is:
6(x+3)−4x−6 = 6x + 18 − 4x − 6 = 2x + 12.

Now we can compare the simplified expressions:
2(x−1)+18 = 2x + 16
6(x+3)−4x−6 = 2x + 12

Both simplified expressions are 2x + a constant term. The constant term is different in each expression (16 in the first and 12 in the second), which means the expressions are not equivalent.

Therefore, 2(x−1)+18 is not equivalent to 6(x+3)−4x−6.