Answered

Ricky looked at his checking account balance regularly. The inequality statement compares the magnitude of his two lowest balances.



$|-300| > |-100|$



What does the inequality statement show?



Select from the drop-down menus to correctly complete the statement:



Even though -300 is [greater / less] than -100, a $100 debt is a [greater / lesser] debt than a $300 debt.

Verified Answer :

  • Recognize that \(|-300| = 300\) and \(|-100| = 100\), so the inequality \(300 > 100\) describes the magnitudes of debt.
  • Identify that \(-300\) is numerically smaller than \(-100\) because it is further to the left on the number line.
  • Observe that a \(\$100\) debt is a smaller amount of money owed compared to a \(\$300\) debt.
  • The completed sentence is: "Even though \(-300\) is numerically less than \(-100\), a \(\$100\) debt is a much lesser debt than a \(\$300\) debt."
  • The final answer is \(\boxed{\text{numerically, much}}\).

Explanation

  1. Analyzing the Problem

We are given the inequality statement \(|-300| > |-100|\). The absolute value \(|x|\) represents the magnitude or distance of a number from zero on the number line. Therefore, \(|-300| = 300\) and \(|-100| = 100\). The inequality \(300 > 100\) compares the sizes of these two debts. We need to fill in the blanks in the sentence: "Even though \(-300\) is [blank 1] less than \(-100\), a \(\$100\) debt is a [blank 2] lesser debt than a \(\$300\) debt."

  1. Completing the Statement

For the first blank, we compare the actual values of \(-300\) and \(-100\). On the number line, \(-300\) is located to the left of \(-100\), which means \(-300 < -100\). Thus, \(-300\) is numerically less than \(-100\). For the second blank, we compare the magnitudes of the debts. A \(\$100\) debt is smaller in amount than a \(\$300\) debt. Therefore, a \(\$100\) debt is a much lesser debt. Thus, the completed sentence is: "Even though \(-300\) is numerically less than \(-100\), a \(\$100\) debt is a much lesser debt than a \(\$300\) debt."

Examples

Understanding the difference between numerical value and absolute magnitude is crucial for managing finances. For example, if you have a balance of -\$50 and your friend has a balance of -\$200, your balance is numerically greater than theirs because -\$50 > -\$200. However, the absolute value of your debt is smaller, meaning you owe less money than your friend. Distinguishing these concepts helps in making informed decisions about debt repayment and budget planning.