Compare Absolute Values: |-25 + 5| vs |20| Equality Check

Question

Are the expressions equal?

25+5  and  20 \left|-25 + 5\right| \; \text{and} \; \left|20\right|

Step-by-Step Solution

First, let's evaluate both expressions separately.

Calculate 25+5\left|-25 + 5\right|:

  • First, simplify inside the absolute value: 25+5=20-25 + 5 = -20.
  • Now take the absolute value of 20-20: 20=20\left|-20\right| = 20 because the absolute value of a negative number is its positive equivalent.

Now, calculate 20\left|20\right|:

  • The number 2020 is already positive, so 20=20\left|20\right| = 20.

Both expressions evaluate to 2020, which means they are equal.

So, the correct answer to the problem is Yes \text{Yes} .

Answer

No