We appreciate your visit to Convert the following inequality into an equation by adding a slack variable tex 7x 1 8x 2 7x 3 leq 145 tex Choose the correct. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
To convert an inequality into an equation using a slack variable, follow these steps:
1. Understand the Requirement:
- You have the inequality: [tex]\(7x_1 + 8x_2 + 7x_3 \leq 145\)[/tex].
- To convert this inequality into an equation, we need to account for the "less than or equal to" part by adding a non-negative slack variable.
2. Add the Slack Variable:
- A slack variable is added to the left side of the inequality. Its purpose is to "take up the slack" or difference between the left and right sides when the inequality is less than the maximum allowable (here 145).
- Let's call the slack variable [tex]\(s_1\)[/tex].
- The expression becomes: [tex]\(7x_1 + 8x_2 + 7x_3 + s_1 = 145\)[/tex].
3. Ensure Non-negativity of the Slack Variable:
- The slack variable [tex]\(s_1\)[/tex] must be greater than or equal to 0, since it represents any "unused" portion between the left side of the original inequality and 145.
4. Choose the Correct Option:
- After adding the slack variable, the inequality is transformed into the equation: [tex]\(7x_1 + 8x_2 + 7x_3 + s_1 = 145\)[/tex].
- This corresponds to the option B.
Thus, the correct corresponding equation after adding the slack variable is:
[tex]\[7x_1 + 8x_2 + 7x_3 + s_1 = 145\][/tex]
Option B is the correct choice.
1. Understand the Requirement:
- You have the inequality: [tex]\(7x_1 + 8x_2 + 7x_3 \leq 145\)[/tex].
- To convert this inequality into an equation, we need to account for the "less than or equal to" part by adding a non-negative slack variable.
2. Add the Slack Variable:
- A slack variable is added to the left side of the inequality. Its purpose is to "take up the slack" or difference between the left and right sides when the inequality is less than the maximum allowable (here 145).
- Let's call the slack variable [tex]\(s_1\)[/tex].
- The expression becomes: [tex]\(7x_1 + 8x_2 + 7x_3 + s_1 = 145\)[/tex].
3. Ensure Non-negativity of the Slack Variable:
- The slack variable [tex]\(s_1\)[/tex] must be greater than or equal to 0, since it represents any "unused" portion between the left side of the original inequality and 145.
4. Choose the Correct Option:
- After adding the slack variable, the inequality is transformed into the equation: [tex]\(7x_1 + 8x_2 + 7x_3 + s_1 = 145\)[/tex].
- This corresponds to the option B.
Thus, the correct corresponding equation after adding the slack variable is:
[tex]\[7x_1 + 8x_2 + 7x_3 + s_1 = 145\][/tex]
Option B is the correct choice.
Thanks for taking the time to read Convert the following inequality into an equation by adding a slack variable tex 7x 1 8x 2 7x 3 leq 145 tex Choose the correct. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
