Question

In order for a pencil to be at a perfect length, it must be within 7/15 of an inch of 6 inches

1. write an equation to show extremes

Answer 1

To find the extremities of the pencil length, we set up an inequality: 6 - 7/15 inches ≤ pencil length ≤ 6 + 7/15 inches. Solving this, we get minimum and maximum lengths of 83/15 inches and 97/15 inches, respectively.

Step-by-step explanation:

To find the extreme lengths of the pencil allowed, we can write an inequality. Since the perfect length is 6 inches, and the pencil can be within 7/15 of an inch of this length, we can use this to set up our equation.

The pencil can either be 7/15 of an inch shorter or longer than 6 inches. This gives us two extremes:

• Minimum length: 6 - 7/15 inches
• Maximum length: 6 + 7/15 inches

To write these as inequalities, we have:

6 - 7/15 ≤ X ≤ 6 + 7/15

Here, X represents the length of the pencil. Now, we can solve for the minimum and maximum lengths:

• Minimum length: 6 - 7/15 = 90/15 - 7/15 = 83/15 inches
• Maximum length: 6 + 7/15 = 90/15 + 7/15 = 97/15 inches