Problem 8 - Elementary Algebra

Question

Simplify the following problems. $$ -|16| $$

Step-by-Step Solution

Answer

Answer: The simplified expression for -|16| is -16.

Step 1: Find the absolute value of 16

First, find the absolute value of 16, which is the distance of 16 from 0 on the number line. The absolute value is represented by the symbol | |, so we have |16| = 16.

Step 2: Multiply by the negative sign

Now, we have to multiply the result from Step 1 by the negative sign outside the absolute value. So, we get -|16| = -(16) = -16.

Step 3: Final Answer

The simplified expression for -|16| is -16.

Key Concepts

Simplifying Expressions

When working with mathematical expressions, the goal often is to make them simpler or easier to understand. This is where simplifying expressions comes into play. It involves reducing an expression to its most basic form. For example, if an expression includes unnecessary symbols or terms, these can be combined or reduced.

In the case of absolute values, simplifying might start with finding the distance of a number from zero and then applying any other operations such as multiplication or addition afterwards. It's much like cleaning up writing by removing extra words that aren't needed. Remember, the simpler the expression, the easier it is to work with in later calculations.

• Simplifying makes solving equations quicker.
• It reduces chances for mistakes in future calculations.
• It provides a clear understanding of the mathematical problem at hand.

Negative Sign

The negative sign in math tells us to take the opposite value of a number. When you see a minus sign (-), it often means to reverse the direction or significance of a number. When combined with absolute values, such as -|16|, it often causes confusion without a deeper understanding.

Here’s how the negative sign works with our example: First, calculate the absolute value of 16, which is 16. Then, apply the negative sign resulting in -16. The negative sign does not change the number itself, just its direction on the number line.

• The negative sign flips the value's direction.
• Pay attention to its position relative to other signs and numbers.
• It turns positive numbers to negative and vice versa.

Number Line Distance

Understanding absolute value involves comprehending the concept of number line distance. Absolute value expressions like |16| represent how far a number is from zero on a number line, regardless of direction. It always results in a positive number or zero.

Imagine a number line:

• Zero is in the center;
• Positive numbers increase to the right;
• Negative numbers extend to the left.

So, when we measure something like |16|, we’re essentially counting 16 units away from zero. It's important to realize that absolute value ignores direction, focusing solely on distance.

• Absolute values are always positive or zero.
• They help in finding how far apart numbers are without considering direction.
• They're crucial in simplifying expressions involving distance.