Question

Please help!

Are the expressions –0.5(3x + 5) and
–1.5x + 2.5 equivalent? Explain why or why not.

Answer 1

Step-by-step explanation: Using the distributive property to expand the first expression, you would get -1.5x - 2.5. Since the constant term does not have the same sign as the second expression, the two expressions are not equivalent. Also, if you substitute in a value for x and evaluate each expression, the values will not be equal.

Answer 2

We can check this two ways: distributing the -0.5, and plugging in a number for x.

First, we can check this by distributing the -0.5. Our equation becomes:

-1.5x -2.5 = -1.5x + 2.5

Clearly, this is not true. We can show this one more time by plugging in a number for x. I will use 2.

Now, we evaluate both sides and see if they are equal.

-3 - 2.5 = -3 + 2.5

-5.5 = 0.5

Clearly, this is not true. These expressions are not equivalent.

Explanation: