Are -(x - 6) and -x - 6 equivalent

Step by step

The question

Question: are −(x − 6) and −x − 6 equivalent?

Equivalent means: the two are equal, whatever number the letter is.

First we simplify the first one: −(x − 6).

We write it shorter, with the same value.

1 Open the brackets

A minus in front of a bracket changes the sign of every part inside.

Now we have −x + 6.

2 Compare

−x + 6 and −x − 6 are not the same.

So no: they are not equivalent.

3 Check

Let's check with a number: x = 2.

The first gives 4.

The second gives −8.

Different.

So the answer is right!

Let's look back.

First: open the brackets.

Then: compare.

Last: check.