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Chapter 2: Problem 28

Evaluate the given expression for \(x=2, y=-3,\) and \(z=-4.\) $$-|z|$$

Short Answer

Expert verified
-4

Step by step solution

01

Substitute the value of z

First, substitute the value of z into the expression. Given that \( z = -4 \), substitute it in: \[ -|-4| \]
02

Evaluate the absolute value

Next, evaluate the absolute value of \( -4 \). The absolute value of \( -4 \) is 4, so the expression becomes: \[ -|4| \]
03

Apply the negative sign

Lastly, apply the negative sign to the absolute value. The negative of 4 is \(-4\), so the final expression is: \[ -4 \]

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Key Concepts

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

Substitute Values
Substituting values is a fundamental concept in algebra. It involves replacing variables in an expression with given numbers. For instance, in the exercise, we need to evaluate the expression for specific values: \(x=2, y=-3,\) and \(z=-4\).

When substituting, ensure to replace the variable carefully:
- Identify the variable and its corresponding value.
- Substitute the variable with its given value in the expression.

In our problem, we substitute \(z\) with \(-4\). The initial expression \(-|z|\) transforms into \(-|-4|\), setting the stage for evaluating the rest of the expression.
Absolute Value
The absolute value of a number refers to its distance from zero on the number line, ignoring its sign. It is always a non-negative number. Consider the absolute value function, denoted by vertical bars: \( |x| \).

Here are some key points:
- The absolute value of a positive number remains the same, e.g., \( |3| = 3 \).
- The absolute value of a negative number turns positive, e.g., \( |-4| = 4 \).
- The absolute value of zero is zero, i.e., \( |0| = 0 \).

In evaluating the absolute value of \(-4\) as in the problem, we get \(|-4| = 4\). Therefore, the expression transforms from \(-|-4|\) to \(-4\).
Negative Numbers
Negative numbers are less than zero and are represented with a minus sign. Understanding how to work with them is crucial in algebra.

Key concepts include:
- The negative of a negative number becomes positive: \(-(-4) = 4\).
- The negative of a positive number remains negative: \(-4 = -4\).

In the final step of our exercise, we apply the negative sign to the absolute value. Since the absolute value of \(-4\) is \(4\), we then apply the negative sign, transforming \(4\) into \(-4\). Thus, the evaluated expression \(-|z|\) simplifies to \(-4\).

Knowing how to handle negative numbers and absolute values are essential skills in algebra, helping you solve a wide range of problems.

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