Problem 111 - Elementary Algebra

Question

Simplify. $$ -|20| $$

Step-by-Step Solution

Answer

-20

Step 1: Understand the Absolute Value

The absolute value of a number represents its distance from zero on a number line, regardless of its direction. Thus, the absolute value of 20, written as \(|20|\), is simply 20.

Step 2: Apply the Negative Sign

Now, multiply the absolute value obtained with the negative sign outside the absolute value bars. This means multiplying 20 by -1, which results in -20.

Key Concepts

Simplifying Expressions

Simplifying expressions is an essential math skill. It involves reducing complex mathematical phrases into simpler form.
In many cases, it means getting rid of any unnecessary elements.

• The purpose is to make computations easier to understand and solve.
• Sometimes, simplifying requires combining like terms or using arithmetic operations.

In the exercise \[-|20|\], simplification involves first computing the absolute value of 20, which is 20.
Next, apply the negative sign to transform the expression into -20.
This step-by-step reduction clarifies the expression's true value, making it easier to interpret and understand.Remember, simplification is a useful tool not only for this exercise but for solving various math problems efficiently.

Negative Sign

A negative sign is a symbol that indicates the opposite value of a number. In math, it plays a significant role in altering the meaning of an expression.

• The negative sign, denoted as '-,' flips the value or direction of a number on the number line.
• When you see a number with a negative sign, it means that number is less than zero, moving it to the left on a number line.
In the expression \(-|20|\), applying the negative sign is a crucial part of simplifying the problem.
Taking \(|20|\) results in 20,but the negative sign changes it to -20.
This small symbol, the negative sign, plays a crucial role in the final value.It's important to pay close attention to how and where negative signs are used in any expression.

Number Line

The number line is a visual tool that helps us understand number positions and values. It stretches indefinitely in both positive and negative directions from zero.

• Positive numbers are to the right of zero, while negative numbers line up to the left.
• This visual tool helps in understanding changes in number values, whether you're moving up or down in value.

The concept of a number line is handy when dealing with absolute values and negative signs.
For instance, finding the absolute value \(|20|\) means identifying how far the number is from zero, emphasizing distance rather than direction.
When calculating, a number line helps you visualize how adding a negative sign shifts that number left, turning 20 into -20. This visual approach simplifies understanding and aids in effectively evaluating expressions.