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Chapter 2: Problem 54

Simplify the expression. $$-|4|$$

Short Answer

Expert verified
-4

Step by step solution

01

- Understand the Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. Thus, \(|4| = 4\).
02

- Apply the Negative Sign

The problem includes a negative sign outside the absolute value. After determining that \(|4| = 4\), apply the negative sign: \(- |4| = -4\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Absolute Value
Absolute value is a mathematical concept that represents the distance of a number from zero on the number line. Unlike regular numbers, absolute value is always non-negative because it measures 'distance'. For example, \( |4| = 4 \). Even if the number is negative, its absolute value is positive. Therefore, \( |-4| = 4 \) too. Think of it as steps you need to walk to reach zero from a point. No matter if you start from -4 or 4, you still need 4 steps.
Working with Negative Numbers
A negative number is any number less than zero, represented with a minus sign. For instance, -4 is a negative number. They show distances or values less than zero. In our problem, after we calculate the absolute value, we also need to think about the outside negative sign. When we have \( - |4| \), it means we need to take the positive result of the absolute value and then apply the negative sign. Hence, \(- |4| = -4\). This step ensures you follow the rule that changing a positive to a negative flips its sign.
Using a Number Line for Visual Clarity
A number line is a helpful tool to visualize numbers. It includes all positive and negative numbers placed sequentially. Zero is at the center, positives to the right, and negatives to the left. For absolute values, the number line helps us see that \( |4| = 4 \), because 4 is 4 units away from zero. Similarly, \( |-4| \) is also 4 units away. When applying negative signs as in \( -|4| \), we start at zero, move 4 units right to positive 4, and then flip left due to the negative sign, ending at -4.

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Most popular questions from this chapter

Divide the real numbers, if possible. $$-48 \div(-6)$$

Fill in the blank with \(<,>,\) or \(=\) $$-8 \square-10$$

Fill in the blank with \(<,>,\) or \(=\) $$-(82) \square|46|$$

Assume \(a>0\) (this means that \(a\) is positive) and \(b<0\) (this means that \(b\) is negative). Find the sign of each expression. $$|a| \div b$$

Fill in the blank with \(<,>,\) or \(=\) $$-|0| \square-|1|$$
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