a while back, either james borrowed $12 from his friend rita or she borrowed $12 from him, but he cant quite…

a while back, either james borrowed $12 from his friend rita or she borrowed $12 from him, but he cant quite remember which. either way, he is planning to pay her back or ask that she pay him back this afternoon. if he has $42.80 in his wallet, which equation represents the amount of money he may have after he sees rita?\n|x - 42.80| = 12\n|x + 42.80| = 12\n|x - 12| = 42.80\n|x + 12| = 42.80

a while back, either james borrowed $12 from his friend rita or she borrowed $12 from him, but he cant quite remember which. either way, he is planning to pay her back or ask that she pay him back this afternoon. if he has $42.80 in his wallet, which equation represents the amount of money he may have after he sees rita?\n|x - 42.80| = 12\n|x + 42.80| = 12\n|x - 12| = 42.80\n|x + 12| = 42.80

Answer

Explanation:

Step1: Analyze the two - case scenarios

Let $x$ be the amount of money James has after seeing Rita. If James borrowed $12$ from Rita, then he will subtract $12$ from his current $42.80$, so $x=42.80 - 12$. If Rita borrowed $12$ from James, then he will add $12$ to his current $42.80$, so $x = 42.80+12$.

Step2: Rewrite in absolute - value form

The absolute - value equation $|x - 42.80|=12$ represents the two possible differences between the final amount $x$ and the initial amount $42.80$. When $x=42.80 + 12$, $|(42.80 + 12)-42.80|=12$, and when $x=42.80 - 12$, $|(42.80 - 12)-42.80|=12$.

Answer:

$|x - 42.80| = 12$