Solve The System Of Inequalities:$ -7x - 50 \leq -1 }$ { -6x + 70 \ \textgreater \ -2 \} Choose One Answer A. { X \geq -7 $ $B. { -7 \leq X \ \textless \ 12 $}$C. { X \ \textless \ 12 $}$D.

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Introduction

In mathematics, solving systems of inequalities is a crucial concept that involves finding the solution set that satisfies multiple inequalities. In this article, we will focus on solving a system of two linear inequalities and provide a step-by-step guide on how to find the solution set.

Understanding the Problem

The given system of inequalities is:

−7x−50≤−1{ -7x - 50 \leq -1 } −6x+70>−2{ -6x + 70 > -2 }

Our goal is to find the solution set that satisfies both inequalities.

Step 1: Simplify the First Inequality

To simplify the first inequality, we can add 50 to both sides:

−7x−50+50≤−1+50{ -7x - 50 + 50 \leq -1 + 50 } −7x≤49{ -7x \leq 49 }

Next, we can divide both sides by -7. However, since we are dividing by a negative number, we need to reverse the direction of the inequality:

x≥−7{ x \geq -7 }

Step 2: Simplify the Second Inequality

To simplify the second inequality, we can add 2 to both sides:

−6x+70+2>−2+2{ -6x + 70 + 2 > -2 + 2 } −6x+72>0{ -6x + 72 > 0 }

Next, we can subtract 72 from both sides:

−6x>−72{ -6x > -72 }

Finally, we can divide both sides by -6. Again, since we are dividing by a negative number, we need to reverse the direction of the inequality:

x<12{ x < 12 }

Step 3: Find the Solution Set

Now that we have simplified both inequalities, we can find the solution set that satisfies both inequalities. To do this, we need to find the intersection of the two solution sets.

The first inequality has a solution set of x≥−7x \geq -7, while the second inequality has a solution set of x<12x < 12. Since both inequalities are true for all values of xx that satisfy both inequalities, the solution set is the intersection of the two solution sets.

Therefore, the solution set is:

−7≤x<12{ -7 \leq x < 12 }

Conclusion

In this article, we have solved a system of two linear inequalities and found the solution set that satisfies both inequalities. We have shown that the solution set is the intersection of the two solution sets and have provided a step-by-step guide on how to find the solution set.

Answer

The correct answer is:

−7≤x<12{ -7 \leq x < 12 }

This corresponds to option B.

Discussion

Solving systems of inequalities is a crucial concept in mathematics that involves finding the solution set that satisfies multiple inequalities. In this article, we have provided a step-by-step guide on how to solve a system of two linear inequalities and have shown that the solution set is the intersection of the two solution sets.

If you have any questions or need further clarification, please feel free to ask.

Additional Resources

For more information on solving systems of inequalities, please refer to the following resources:

  • Khan Academy: Solving Systems of Linear Inequalities
  • Mathway: Solving Systems of Linear Inequalities
  • Wolfram Alpha: Solving Systems of Linear Inequalities

Related Topics

  • Solving Systems of Linear Equations
  • Graphing Linear Inequalities
  • Solving Quadratic Inequalities

FAQs

  • Q: What is the solution set for the system of inequalities? A: The solution set is −7≤x<12-7 \leq x < 12.
  • Q: How do I find the solution set for a system of inequalities? A: To find the solution set, you need to find the intersection of the two solution sets.
  • Q: What is the intersection of two solution sets? A: The intersection of two solution sets is the set of values that satisfy both inequalities.
    Frequently Asked Questions (FAQs) on Solving Systems of Inequalities ====================================================================

Introduction

Solving systems of inequalities is a crucial concept in mathematics that involves finding the solution set that satisfies multiple inequalities. In this article, we will provide a comprehensive list of frequently asked questions (FAQs) on solving systems of inequalities, along with detailed answers to help you better understand the concept.

Q&A

Q1: What is a system of inequalities?

A system of inequalities is a set of two or more inequalities that are related to each other. In this article, we will focus on solving systems of two linear inequalities.

Q2: How do I solve a system of inequalities?

To solve a system of inequalities, you need to find the solution set that satisfies both inequalities. This involves simplifying each inequality, finding the solution set for each inequality, and then finding the intersection of the two solution sets.

Q3: What is the intersection of two solution sets?

The intersection of two solution sets is the set of values that satisfy both inequalities. In other words, it is the set of values that are common to both solution sets.

Q4: How do I find the intersection of two solution sets?

To find the intersection of two solution sets, you need to find the values that satisfy both inequalities. This involves comparing the two solution sets and finding the values that are common to both.

Q5: What is the solution set for a system of inequalities?

The solution set for a system of inequalities is the set of values that satisfy both inequalities. In other words, it is the set of values that are common to both solution sets.

Q6: How do I graph a system of inequalities?

To graph a system of inequalities, you need to graph each inequality separately and then find the intersection of the two graphs.

Q7: What is the difference between a system of linear inequalities and a system of quadratic inequalities?

A system of linear inequalities involves linear inequalities, while a system of quadratic inequalities involves quadratic inequalities. Solving a system of quadratic inequalities is more complex than solving a system of linear inequalities.

Q8: How do I solve a system of quadratic inequalities?

To solve a system of quadratic inequalities, you need to factor the quadratic expressions, find the solution set for each inequality, and then find the intersection of the two solution sets.

Q9: What is the importance of solving systems of inequalities?

Solving systems of inequalities is important in mathematics and real-world applications. It helps us to model and solve problems that involve multiple constraints.

Q10: How do I apply solving systems of inequalities in real-world applications?

Solving systems of inequalities can be applied in various real-world applications, such as:

  • Modeling and solving problems in economics, finance, and business
  • Solving problems in engineering, physics, and computer science
  • Modeling and solving problems in biology, medicine, and healthcare

Conclusion

Solving systems of inequalities is a crucial concept in mathematics that involves finding the solution set that satisfies multiple inequalities. In this article, we have provided a comprehensive list of frequently asked questions (FAQs) on solving systems of inequalities, along with detailed answers to help you better understand the concept.

Additional Resources

For more information on solving systems of inequalities, please refer to the following resources:

  • Khan Academy: Solving Systems of Linear Inequalities
  • Mathway: Solving Systems of Linear Inequalities
  • Wolfram Alpha: Solving Systems of Linear Inequalities

Related Topics

  • Solving Systems of Linear Equations
  • Graphing Linear Inequalities
  • Solving Quadratic Inequalities

Glossary

  • System of inequalities: A set of two or more inequalities that are related to each other.
  • Solution set: The set of values that satisfy both inequalities.
  • Intersection: The set of values that are common to both solution sets.
  • Linear inequality: An inequality that involves a linear expression.
  • Quadratic inequality: An inequality that involves a quadratic expression.

FAQs Categories

  • General FAQs: General questions about solving systems of inequalities.
  • Graphing FAQs: Questions about graphing systems of inequalities.
  • Solving FAQs: Questions about solving systems of inequalities.
  • Real-world applications: Questions about applying solving systems of inequalities in real-world applications.