Question

a pending cash booking of a user’s current balance. juan’s and greg’s current balances (in dollars) are shown on the number line. a positive balance means there is money in the account. a negative balance represents debt. (a) find the absolute value of the account balance for each person. juan: $|-84| = $ greg: $|-45| = $ (b) which person has a larger debt?
\t- juan
\t- greg
\t- neither has a larger debt.

Explanation:

Step1: Recall absolute value definition

The absolute value of a number \( x \), denoted \( |x| \), is the distance from \( x \) to 0 on the number line, so \( |x| = x \) if \( x \geq 0 \) and \( |x| = -x \) if \( x < 0 \).

Step2: Calculate absolute value for Jace

For \( | - 84| \), since \( -84 < 0 \), we use \( |x|=-x \). So \( | - 84|=-(-84) = 84 \).

Step3: Calculate absolute value for Greng

For \( | - 45| \), since \( -45 < 0 \), we use \( |x|=-x \). So \( | - 45|=-(-45) = 45 \).

Step4: Compare absolute values

We compare 84 and 45. Since \( 84>45 \), the absolute value of Jace's balance is larger, meaning Jace has a larger debt (because debt is represented by negative balances, and larger absolute value of a negative number means a larger debt).

Answer:

(a) Jace: \( | - 84| = 84 \); Greng: \( | - 45| = 45 \)
(b) Jace