Final answer:
To find the largest possible integer so that the difference of the integer and 46 is at most 153, set up an inequality using absolute value. Solve the inequality and determine the range of possible values for the integer. The largest possible integer is 199.
Step-by-step explanation:
To find the largest possible integer so that the difference of the integer and 46 is at most 153, we can set up an inequality. Let the integer be represented by x. The inequality is then: |x - 46| ≤ 153.
- Simplify the inequality by removing the absolute value brackets. This gives us two separate inequalities: x - 46 ≤ 153 and -(x - 46) ≤ 153.
- Solve each inequality separately for x. For the first inequality, add 46 to both sides to get x ≤ 199. For the second inequality, distribute the negative sign and add 46 to both sides to get x ≥ -107.
- The largest possible integer can be any value between -107 and 199, inclusive. Therefore, the largest possible integer is 199.