Read the inequality carefully

Oct 13, 2025 by miodeya.com 18 views

Introduction

In mathematics, inequalities are used to describe relationships between variables. They are an essential part of algebra and are used to solve a wide range of problems. In this article, we will explore whether the point (8,-5) makes the inequality 10x + 14y ≤ 10 true. To do this, we will substitute the values of x and y into the inequality and determine if the statement is true or false.

Understanding the Inequality

The given inequality is 10x + 14y ≤ 10. This is a linear inequality, which means it can be graphed as a line on a coordinate plane. The inequality states that the sum of 10 times x and 14 times y is less than or equal to 10. In other words, the point (x,y) must lie on or below the line defined by the equation 10x + 14y = 10.

Substituting the Values of x and y

To determine if the point (8,-5) makes the inequality true, we need to substitute the values of x and y into the inequality. We will replace x with 8 and y with -5, and then simplify the expression.

10(8) + 14(-5) ≤ 10

Evaluating the Expression

Now, we will evaluate the expression by multiplying 10 and 8, and 14 and -5.

80 - 70 ≤ 10

Simplifying the Expression

Next, we will simplify the expression by combining the terms.

10 ≤ 10

Conclusion

The final result is 10 ≤ 10, which is a true statement. This means that the point (8,-5) makes the inequality 10x + 14y ≤ 10 true.

Why is this Important?

Understanding how to evaluate inequalities is crucial in mathematics and real-world applications. Inequalities are used to model a wide range of problems, from finance to science. By being able to evaluate inequalities, we can make informed decisions and solve complex problems.

Tips for Evaluating Inequalities

Here are some tips for evaluating inequalities:

Read the inequality carefully: Make sure you understand what the inequality is saying.
Substitute the values of x and y: Replace x with the given value and y with the given value.
Simplify the expression: Combine like terms and evaluate any expressions.
Determine if the statement is true or false: If the final result is true, then the point makes the inequality true.

Conclusion

In conclusion, the point (8,-5) makes the inequality 10x + 14y ≤ 10 true. By understanding how to evaluate inequalities, we can solve complex problems and make informed decisions. Remember to read the inequality carefully, substitute the values of x and y, simplify the expression, and determine if the statement is true or false.

Frequently Asked Questions

What is an inequality? An inequality is a statement that describes a relationship between variables. It can be used to model a wide range of problems, from finance to science.
How do I evaluate an inequality? To evaluate an inequality, you need to substitute the values of x and y into the inequality, simplify the expression, and determine if the statement is true or false.
What is the difference between a linear inequality and a quadratic inequality? A linear inequality is an inequality that can be graphed as a line on a coordinate plane. A quadratic inequality is an inequality that can be graphed as a parabola on a coordinate plane.

Final Thoughts

In conclusion, understanding how to evaluate inequalities is crucial in mathematics and real-world applications. By being able to evaluate inequalities, we can make informed decisions and solve complex problems. Remember to read the inequality carefully, substitute the values of x and y, simplify the expression, and determine if the statement is true or false.

Introduction

In the previous article, we explored whether the point (8,-5) makes the inequality 10x + 14y ≤ 10 true. In this article, we will answer some frequently asked questions about inequalities.

Q&A

Q: What is an inequality?

A: An inequality is a statement that describes a relationship between variables. It can be used to model a wide range of problems, from finance to science.

Q: How do I evaluate an inequality?

A: To evaluate an inequality, you need to substitute the values of x and y into the inequality, simplify the expression, and determine if the statement is true or false.

Q: What is the difference between a linear inequality and a quadratic inequality?

A: A linear inequality is an inequality that can be graphed as a line on a coordinate plane. A quadratic inequality is an inequality that can be graphed as a parabola on a coordinate plane.

Q: How do I graph an inequality on a coordinate plane?

A: To graph an inequality on a coordinate plane, you need to graph the equation that defines the inequality. Then, you need to shade the region that satisfies the inequality.

Q: What is the significance of inequalities in real-world applications?

A: Inequalities are used to model a wide range of problems, from finance to science. They are used to make informed decisions and solve complex problems.

Q: Can inequalities be used to solve systems of equations?

A: Yes, inequalities can be used to solve systems of equations. By using inequalities, you can find the solution to a system of equations that is not possible using equations alone.

Q: How do I solve a system of inequalities?

A: To solve a system of inequalities, you need to find the solution that satisfies all the inequalities. This can be done by graphing the inequalities on a coordinate plane and finding the region that satisfies all the inequalities.

Q: What is the difference between a strict inequality and a non-strict inequality?

A: A strict inequality is an inequality that is written with a strict symbol, such as < or >. A non-strict inequality is an inequality that is written with a non-strict symbol, such as ≤ or ≥.

Q: Can inequalities be used to model real-world problems that involve uncertainty?

A: Yes, inequalities can be used to model real-world problems that involve uncertainty. By using inequalities, you can represent the uncertainty in a problem and find the solution that satisfies the inequality.

Conclusion

In conclusion, inequalities are an essential part of mathematics and are used to model a wide range of problems, from finance to science. By understanding how to evaluate and graph inequalities, you can make informed decisions and solve complex problems. Remember to read the inequality carefully, substitute the values of x and y, simplify the expression, and determine if the statement is true or false.

Final Thoughts

Inequalities are a powerful tool for modeling real-world problems. By using inequalities, you can represent uncertainty and find the solution that satisfies the inequality. Remember to graph the inequality on a coordinate plane, substitute the values of x and y, simplify the expression, and determine if the statement is true or false.

Tips for Evaluating Inequalities

Here are some tips for evaluating inequalities:

Read the inequality carefully: Make sure you understand what the inequality is saying.
Substitute the values of x and y: Replace x with the given value and y with the given value.
Simplify the expression: Combine like terms and evaluate any expressions.
Determine if the statement is true or false: If the final result is true, then the point makes the inequality true.