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Chapter 1: Problem 208

Evaluate. a) \(-|a|\) when \(a=60\) b) \(-|b|\) when \(b=-12\)

Short Answer

Expert verified
a) \-|60| = -60\. b) \-|-12| = -12\.

Step by step solution

01

- Understand Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always a non-negative value. The absolute value of a number is denoted as \(|a|\).
02

- Evaluate Absolute Value for 'a'

Given that \(a = 60\), calculate \(|a|\). Since 60 is already positive, \(|60| = 60\).
03

- Apply Negative Sign for 'a'

Next, apply the negative sign as given in the problem. Therefore, \(-|a| = -60\).
04

- Evaluate Absolute Value for 'b'

Given that \(b = -12\), calculate \(|b|\). Since \(|-12| = 12\).
05

- Apply Negative Sign for 'b'

Finally, apply the negative sign as given in the problem. Therefore, \(-|b| = -12\).

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Key Concepts

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

algebra basics
Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.
It's like a language that helps us describe mathematical relationships.
These symbols can represent numbers, variables, and operations.
Here are some fundamentals of algebra to get you started:
  • **Variables**: Symbols (like \(x\) or \(a\)) that stand in for unknown values.
  • **Constants**: Fixed values that don't change.
  • **Expressions**: Combinations of variables, constants, and operations (like \(3x + 4\)).
  • **Equations**: Statements that two expressions are equal (like \(3x + 4 = 7\)).

In the given exercise, we're dealing with an expression involving absolute values and negative signs.
positive and negative numbers
Positive and negative numbers are used to describe values on either side of zero on a number line.
Positive numbers are greater than zero, while negative numbers are less than zero.
Here are some points to remember:
  • **Positive Numbers**: Numbers like 1, 2, 3, etc.
  • **Negative Numbers**: Numbers like -1, -2, -3, etc.
  • **Zero**: Neither positive nor negative.

In the exercise, we have both positive and negative numbers: \(a = 60\) (positive) and \(b = -12\) (negative).
The absolute value of a number is its distance from zero, making it always non-negative.
So, the absolute value of \(60\) is \(60\), and the absolute value of \(-12\) is \(12\).
evaluating expressions
Evaluating expressions involves finding the value of an expression given specific values for the variables.
Here's how we do it:
  • **Step 1**: Substitute the given values into the expression.
  • **Step 2**: Perform any operations within absolute value symbols.
  • **Step 3**: Apply additional operations like addition, subtraction, etc.

For example, let's evaluate \(-|a|\) when \(a = 60\):
  • Calculate \|a|\: since a is 60, \[|60|=60\]\

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