Explain the difference in meaning between |-3| and -3. In your explanation, be sure to include various key words you learned within this unit.

The difference in meaning is that

-3 is a signed value. It lies to the left of zero

+3 is also a signed value, and since it is positive, it lies to the right of zero

|-3| is just the physical distance (left or right) of -3 from zero. Since we live in a physical world, all distances are positive, so its signed value is 3.

Since +3 is also 3 units from zero, |+3| = 3

|-3| = |+3| = 3 since both are three units away from zero.

So, when using absolute values as numbers, rather than distances,

|x| = x if x is not negative
|x| = -x if x is negative

on number line |-3| is 3 units right of zero

but
-3 is 3 units left of zero
so the difference is 6 units.

Ah, the difference between |-3| and -3, you've stumbled into an intriguing mathematical circus, my friend! Let's step right into the ring and unravel this mystery.

First things first, |-3|, also known as the absolute value of -3, is like a mathematical bungee jump that prevents negativity from dragging us down. It's like putting a happy clown mask on a potentially sad number. The absolute value function basically strips away the negativity and gives us a positive result in return. So |-3| equals 3, essentially saying "hey negative, take a hike, we only want the positive vibes here!"

On the other hand, -3 is a humble little negative number just minding its own business, without any fancy absolute value tricks. It's the number you get when you subtract 3 from 0, or simply the opposite of the number 3.

So to summarize, |-3| jumps through hoops to give us the positive result of 3, while -3 is content being its negative self. Think of them as two performers in the circus of numbers, each with its own unique style and purpose.

Remember, in the world of math, absolute value is like a clown nose that always brings out the positive side of a number, while negatives are the quiet introverts of the numerical community, happily dwelling on the less sunny side of life.

To understand the difference in meaning between |-3| and -3, let's start by introducing some key terms related to absolute value and negative numbers.

Absolute value refers to the magnitude or size of a number without considering its sign. It is denoted by vertical bars or absolute value symbols, such as |x|. The absolute value of a number is always positive or zero.

Negative numbers, on the other hand, represent values that are less than zero. They are generally denoted with a minus sign (-) placed before the number.

Now, let's apply these concepts to |-3| and -3:

1. |-3|: This expression represents the absolute value of -3. The vertical bars around -3 indicate that we are interested in its magnitude, regardless of its sign. Therefore, |-3| equals 3, because the magnitude of -3 is 3. It is important to note that the absolute value of -3 is positive.

2. -3: This is a negative number. It simply represents the value of -3 itself, without accounting for its magnitude. The minus sign in front of the number indicates that it is negative.

In summary, |-3| represents the absolute value of -3, which gives the positive magnitude of -3 (in this case, 3), while -3 is a negative number itself, indicating a value less than zero.