Question

A machine at a metal shop mill cuts rods that are 4.25 meters long. It is acceptable forthe length to differ from this value by at most 0.02 meters. I need this to be answered in absolute value for part 1 For part 2 I need the absolute inequality and compound inequality answers using l

Answer 1

We are given the standard length of the metal rods cut by a machine and it is 4.25m. The acceptable deviation is 0.02m.

Roughly, we can state this as L = 4.25 ± 0.02. This means that the length can be anywhere from 4.23m to 4.27m. We can write this inequality as:

$4.23\leq L\leq4.27$

But because we need the inequality to be stated in absolute value terms, we write:

$|L-4.25|\leq0.02$

When solving for this inequality, we actually go back to the previous inequality, which tells us that we got it correctly.

$\begin{gathered} |L-4.25|\leq0.02 \\ \\ -0.02\leq L-4.25\leq0.02 \\ \\ 4.23\leq L\leq4.27 \end{gathered}$