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Chapter 1: Problem 83

Determine whether each statement is true or false. \(-|-5| \geq-|-9|\)

Short Answer

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Step by step solution

01

Understand Absolute Value

Recall that the absolute value of a number is its distance from zero on the number line, regardless of direction. For any number x, \(-|x| = -|x|\).
02

Calculate Absolute Values

Determine the absolute values of -5 and -9: \(|-5| = 5\) and \(|-9| = 9\). Therefore, \(-|-5| = -5\) and \(-|-9| = -9\).
03

Compare the Values

Now compare the values: Is \(-5 \geq -9\) true or false? Since -5 is greater than -9 on the number line, this statement is true.

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Key Concepts

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

absolute value
The absolute value of a number refers to its distance from zero on the number line, without considering the direction.
It is always a non-negative number. For example, the absolute value of both 5 and -5 is 5, denoted as \(|5| = 5\). This concept of distance helps in simplifying expressions and solving equations.
When dealing with absolute values, the symbol |x| is used to signify the absolute magnitude of the number x.
number line
A number line is a straight, horizontal line that illustrates numbers at equal intervals.
It extends infinitely in both positive and negative directions. Zero is positioned at the center, serving as a reference point.
Positive numbers are to the right of zero, while negative numbers are to the left:
  • Each point on the number line corresponds to a unique real number.
  • The distance between any two points on the line represents the difference in their values.
  • Absolute values can be easily compared using a number line.

For example, on the number line, -5 is to the left of -9, indicating that -5 is greater than -9.
inequalities
Inequalities are mathematical expressions that show the relationship between two values where they are not equal. Common symbols include:
  • \(>\) meaning greater than
  • \(<\) meaning less than
  • \(\geq\) meaning greater than or equal to
  • \(\leq\) meaning less than or equal to

Inequalities are used to compare numbers or expressions and are displayed on a number line.
For example, in the statement \(-5 \geq -9\), it means -5 is greater than or equal to -9. This is true because, on the number line, -5 is positioned to the right of -9.

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Most popular questions from this chapter

Use the distributive property to rewrite each expression. $$ -5.2(4 x+2.3) $$

Write a numerical expression for each phrase, and simplify the expression. -2 added to the sum of -18 and 11

Use the distributive property to rewrite each expression. $$ 8(3 r+4 s-5 y) $$

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(6 x-5 y+4 a\)

Solve each problem. Marcial owes \(\$ 679.00\) on his Visa account. He returns three items costing \(\$ 36.89, \$ 29.40\), and \(\$ 113.55\) and receives credit for these on the account. Next, he makes purchases of \(\$ 135.78\) and \(\$ 412.88\) and two purchases of \(\$ 20.00\) each. He makes a payment of \(\$ 400\). He then incurs a finance charge of \(\$ 24.57 .\) How much does he still owe?
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