Algebra-1

To find the inequality that shows the range of allowable weights for a bag of sugar, we need to set up the absolute value inequality.

Let w be the weight of a bag of sugar.

Given:

Any bag that varies from the weight by more than 10g is sent back.

This means the difference between the weight w and the target weight of 1000g should be less than or equal to 10.

Then, we can set up the inequality:

|w - 1000| ≤ 10

For an inequality of the form |A| ≤ B, where A is an expression and B is a positive number, it can be rewritten as a compound inequality: -B ≤ A ≤ B. This inequality can be written as: -10 ≤ w - 1000 ≤ 10.