Let's break down the steps to understand how we find the range of acceptable lengths for the steel plates.
1. Problem Understanding:
- The target length of the steel plates is 11.93 meters.
- The acceptable error margin is ±0.02 meters.
2. Setting Up the Inequality:
- We are dealing with an absolute value inequality to represent the acceptable range.
- The standard form of the inequality should be [tex]\(\mid x - \text{target length} \mid \leq \text{error margin}\)[/tex].
3. Filling in Values:
- Target length = 11.93 meters
- Error margin = 0.02 meters
Therefore, the inequality becomes [tex]\(\mid x - 11.93 \mid \leq 0.02\)[/tex].
4. Solving the Inequality:
- To solve this absolute value inequality, we need to break it down into two separate inequalities:
[tex]\[
-0.02 \leq x - 11.93 \leq 0.02
\][/tex]
- Next, we solve these two inequalities.
5. Calculate the Bounds:
- For the lower bound:
[tex]\[
-0.02 \leq x - 11.93 \implies x \geq 11.93 - 0.02 \implies x \geq 11.91
\][/tex]
- For the upper bound:
[tex]\[
x - 11.93 \leq 0.02 \implies x \leq 11.93 + 0.02 \implies x \leq 11.95
\][/tex]
6. Writing the Range:
- Combining these results, we get the range of acceptable lengths:
[tex]\(
11.91 \leq x \leq 11.95
\)[/tex]
So, the inequality and the range of acceptable lengths are:
- The inequality is [tex]\(\mid x - 11.93 \mid \leq 0.02 \)[/tex].
- The range of acceptable lengths is [tex]\(11.91 \leq x \leq 11.95\)[/tex].
Now, filling the boxes:
1. The inequality [tex]\(\mid x- \boxed{11.93} \mid \leq \boxed{0.02}\)[/tex] can be used to find the range of acceptable lengths for the steel plates.
2. The range of acceptable lengths for the steel plates is [tex]\(\boxed{11.91} \leq x \leq \boxed{11.95}\)[/tex].
I hope this clarifies the steps involved in solving this question!
