Can someone explain this:
Which symbol will make |-6| ? -6 true?
( = > < )
Also
Which symbol will make the number sentence -|16| ? 16 true?
Thanks :)
The first one would be the more than sign (>) because |-6| is the absolute value. The second one would be equal to sign (=) because the absolute value of -16 is positive 16. Hope I helped! :-)
-|16| < 16
because -|16| = -16
Note -- it does not say |-16|
Sure, I'll explain it in a clowny way!
For the first question, let's find out which symbol will make |-6| ? -6 true. Well, |-6| means the absolute value of -6, which is always positive. And -6 is definitely not positive. So, no matter which symbol you choose (=, >, or <), it won't make |-6| equal to -6. It's like trying to make a grumpy cat smile - it's just not going to happen!
Now let's move to the second question. We have -|16| ? 16. Again, |-16| gives us a positive value, so we have -positive ? 16. The only symbol that can make it true is <, because -positive is always less than any positive number. It's like saying, "Hey -16, try to be as little as possible!" and it can only be less than 16.
I hope that brings a little laughter to your math questions! Don't forget to juggle some numbers too!
To determine which symbol makes the given number sentence true, we need to understand the meaning of the absolute value and how it interacts with inequalities.
Absolute value:
The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. Symbolically, |-x| = x if x is greater than or equal to zero, and |-x| = -x if x is less than zero.
In the first question, we are asked to find the symbol that makes |-6| ? -6 true. Let's break it down:
|-6| = ?
Here, since 6 is a negative number, |-6| = -6 according to the definition of the absolute value. Therefore, -6 is the correct answer. Now, we need to determine which symbol makes |-6| -6 true.
We can rewrite the inequality as |-6| ? -6. Since |-6| equals -6, the correct symbol to make the inequality true is =.
Therefore, |-6| = -6 is true.
In the second question, we are asked to find the symbol that makes the number sentence -|16| ? 16 true. Here's how we can figure it out:
-|16| = ?
Since 16 is a positive number, |-16| = 16 according to the definition of absolute value. However, we have a negative sign in front of the absolute value in the number sentence. Therefore, we need the result to be negative.
So, -|16| = -16.
Now, we need to determine which symbol makes -|16| ? 16 true.
Since -16 is less than 16, the correct symbol to make the inequality true is <.
Therefore, -|16| < 16 is true.
I hope this explanation helps clarify the concept of absolute value and how it relates to inequalities. Feel free to ask if you have any further questions!