Final answer:
To determine the range of money you could have, set up the absolute value equation |x - 1500| = 100. Solve for x to find that you could have either 1400 or 1600 pesos, meaning you must have between these two amounts inclusive.
Step-by-step explanation:
To find the least and greatest amount of money you could have in your wallet, given that you have 1500 pesos with a possible error of 100 pesos in either direction, you can set up an absolute value equation. The absolute value of a number represents its distance from zero on the number line without considering direction, so it's perfect for this situation.
The equation would be |x - 1500| = 100, where x represents the actual amount of money you have. To solve this equation, consider the two scenarios- the amount is 100 more or 100 less than 1500.
The first scenario is x - 1500 = 100, which means x = 1600. So, one possibility is that you have 1600 pesos.
The second scenario is x - 1500 = -100, which means x = 1400. This gives us the other possibility, that you have 1400 pesos.
Therefore, the least amount you might have is 1400 pesos, and the greatest amount might be 1600 pesos.