Thank you for visiting The rules state that the weight of the suitcase can vary by at most 7 5 pounds Write an inequality you could use to find. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To solve this problem, we want to determine the range of acceptable weights [tex]\(x\)[/tex] for the suitcase, knowing that it can vary by at most 7.5 pounds from the desired weight of 40 pounds.
### Step-by-Step Solution
1. Define the Acceptable Deviation:
- The weight of the suitcase can vary by at most 7.5 pounds from 40 pounds.
2. Set Up the Inequality:
- We express this as an absolute value inequality. If [tex]\(x\)[/tex] is the weight of the suitcase, then the deviation from 40 pounds should be within 7.5 pounds. Mathematically, this is represented as:
[tex]\[
|x - 40| \leq 7.5
\][/tex]
3. Solve the Absolute Value Inequality:
- An absolute value inequality of the form [tex]\(|A| \leq B\)[/tex] translates to two separate inequalities:
[tex]\[
-B \leq A \leq B
\][/tex]
- Applying this to our inequality:
[tex]\[
-7.5 \leq x - 40 \leq 7.5
\][/tex]
4. Isolate [tex]\(x\)[/tex]:
- To find the range for [tex]\(x\)[/tex], we solve these two inequalities separately.
For the lower bound:
[tex]\[
-7.5 \leq x - 40
\][/tex]
Adding 40 to both sides:
[tex]\[
32.5 \leq x
\][/tex]
For the upper bound:
[tex]\[
x - 40 \leq 7.5
\][/tex]
Adding 40 to both sides:
[tex]\[
x \leq 47.5
\][/tex]
5. Combine the Results:
- Combining both results, we get the range for [tex]\(x\)[/tex]:
[tex]\[
32.5 \leq x \leq 47.5
\][/tex]
### Final Answer
To find the range of acceptable weights for your suitcase where [tex]\(x\)[/tex] is the weight of the suitcase, the inequality can be written as:
[tex]\[
|x - 40| \leq 7.5
\][/tex]
And the range of acceptable weights [tex]\(x\)[/tex] is:
[tex]\[
32.5 \leq x \leq 47.5
\][/tex]
This means the suitcase can weigh anywhere between 32.5 pounds and 47.5 pounds inclusively.
### Step-by-Step Solution
1. Define the Acceptable Deviation:
- The weight of the suitcase can vary by at most 7.5 pounds from 40 pounds.
2. Set Up the Inequality:
- We express this as an absolute value inequality. If [tex]\(x\)[/tex] is the weight of the suitcase, then the deviation from 40 pounds should be within 7.5 pounds. Mathematically, this is represented as:
[tex]\[
|x - 40| \leq 7.5
\][/tex]
3. Solve the Absolute Value Inequality:
- An absolute value inequality of the form [tex]\(|A| \leq B\)[/tex] translates to two separate inequalities:
[tex]\[
-B \leq A \leq B
\][/tex]
- Applying this to our inequality:
[tex]\[
-7.5 \leq x - 40 \leq 7.5
\][/tex]
4. Isolate [tex]\(x\)[/tex]:
- To find the range for [tex]\(x\)[/tex], we solve these two inequalities separately.
For the lower bound:
[tex]\[
-7.5 \leq x - 40
\][/tex]
Adding 40 to both sides:
[tex]\[
32.5 \leq x
\][/tex]
For the upper bound:
[tex]\[
x - 40 \leq 7.5
\][/tex]
Adding 40 to both sides:
[tex]\[
x \leq 47.5
\][/tex]
5. Combine the Results:
- Combining both results, we get the range for [tex]\(x\)[/tex]:
[tex]\[
32.5 \leq x \leq 47.5
\][/tex]
### Final Answer
To find the range of acceptable weights for your suitcase where [tex]\(x\)[/tex] is the weight of the suitcase, the inequality can be written as:
[tex]\[
|x - 40| \leq 7.5
\][/tex]
And the range of acceptable weights [tex]\(x\)[/tex] is:
[tex]\[
32.5 \leq x \leq 47.5
\][/tex]
This means the suitcase can weigh anywhere between 32.5 pounds and 47.5 pounds inclusively.
Thank you for reading the article The rules state that the weight of the suitcase can vary by at most 7 5 pounds Write an inequality you could use to find. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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Rewritten by : Jeany
