Question

ABSOLUTE VALUE. Mona claims that |m-n| is always equal to |m| - |n|. Give me two numbers to represent m and n that would prove Mona wrong.

a) m = 5, n = 3
b) m = -2, n = 6
c) m = 4, n = -1
d) m = 0, n = 0

Answer 1

The claim that |m-n| is always equal to |m| - |n| is incorrect. By choosing m = -2 and n = 6, we find that |m-n| equals 8, whereas |m| - |n| equals -4, showing the values are not equal.

Step-by-step explanation:

You asked if |m-n| is always equal to |m| - |n|. The claim by Mona is incorrect, and we can demonstrate this using an example from the options provided. Let's pick option b) m = -2, n = 6.

To calculate the absolute value of the difference |m-n|, we first find the difference between m and n, and then take the absolute value. So for m = -2 and n = 6, we do the following calculation:

• |m-n| = |-2 - 6| = |-8| = 8

Next, we'll calculate |m| - |n| by finding the absolute value of each number and then subtracting:

• |m| = |-2| = 2
• |n| = |6| = 6
• |m| - |n| = 2 - 6 = -4

Comparing our results, we can see that |m-n| = 8 whereas |m| - |n| = -4. These values are clearly not equal, hence proving Mona's claim wrong.