In Which Set Do All Of The Values Make The Inequality 2 X − 1 \textless 10 2x - 1 \ \textless \ 10 2 X − 1 \textless 10 True?

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Introduction

In mathematics, inequalities are used to compare the values of different expressions. They are an essential part of algebra and are used to solve a wide range of problems. In this article, we will focus on the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 and determine in which set all of the values make this inequality true.

Understanding the Inequality

The given inequality is 2x−1 \textless 102x - 1 \ \textless \ 10. To solve this inequality, we need to isolate the variable xx. We can start by adding 11 to both sides of the inequality, which gives us 2x \textless 112x \ \textless \ 11. Next, we can divide both sides of the inequality by 22, which gives us x \textless 5.5x \ \textless \ 5.5.

Solving the Inequality

Now that we have isolated the variable xx, we can determine the set of values that make the inequality true. The inequality x \textless 5.5x \ \textless \ 5.5 is true for all values of xx that are less than 5.55.5. This means that the set of values that make the inequality true is the set of all real numbers less than 5.55.5.

Writing the Solution in Interval Notation

We can write the solution in interval notation as (−∞,5.5)(-\infty, 5.5). This notation indicates that the solution is the set of all real numbers that are less than 5.55.5.

Understanding the Solution

The solution (−∞,5.5)(-\infty, 5.5) indicates that all values of xx that are less than 5.55.5 make the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 true. This means that any value of xx that is less than 5.55.5 will satisfy the inequality.

Example

Let's consider an example to illustrate the solution. Suppose we want to find the values of xx that make the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 true. We can substitute different values of xx into the inequality and determine whether it is true or false.

For example, if we let x=5x = 5, we get 2(5)−1=92(5) - 1 = 9, which is not less than 1010. Therefore, the value x=5x = 5 does not make the inequality true.

On the other hand, if we let x=4x = 4, we get 2(4)−1=72(4) - 1 = 7, which is less than 1010. Therefore, the value x=4x = 4 makes the inequality true.

Conclusion

In conclusion, the set of values that make the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 true is the set of all real numbers less than 5.55.5. This can be written in interval notation as (−∞,5.5)(-\infty, 5.5). We can use this solution to determine the values of xx that satisfy the inequality.

Frequently Asked Questions

  • What is the solution to the inequality 2x−1 \textless 102x - 1 \ \textless \ 10?
  • The solution to the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 is the set of all real numbers less than 5.55.5.
  • How can we write the solution in interval notation?
  • The solution can be written in interval notation as (−∞,5.5)(-\infty, 5.5).
  • What values of xx make the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 true?
  • Any value of xx that is less than 5.55.5 makes the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 true.

Final Thoughts

In this article, we have discussed the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 and determined the set of values that make it true. We have also written the solution in interval notation and provided examples to illustrate the solution. We hope that this article has provided a clear understanding of the solution to the inequality and has been helpful in solving similar problems.

Introduction

In our previous article, we discussed the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 and determined the set of values that make it true. In this article, we will answer some frequently asked questions related to the inequality.

Q&A

Q: What is the solution to the inequality 2x−1 \textless 102x - 1 \ \textless \ 10?

A: The solution to the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 is the set of all real numbers less than 5.55.5. This can be written in interval notation as (−∞,5.5)(-\infty, 5.5).

Q: How can we write the solution in interval notation?

A: The solution can be written in interval notation as (−∞,5.5)(-\infty, 5.5). This notation indicates that the solution is the set of all real numbers that are less than 5.55.5.

Q: What values of xx make the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 true?

A: Any value of xx that is less than 5.55.5 makes the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 true.

Q: Can we find the solution to the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 using a graph?

A: Yes, we can find the solution to the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 using a graph. We can graph the equation 2x−1=102x - 1 = 10 and determine the values of xx that make the inequality true.

Q: How can we use the solution to the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 to solve a problem?

A: We can use the solution to the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 to solve a problem by substituting different values of xx into the inequality and determining whether it is true or false.

Q: Can we use the solution to the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 to solve a system of inequalities?

A: Yes, we can use the solution to the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 to solve a system of inequalities. We can graph the solution to the inequality and determine the values of xx that make the system of inequalities true.

Q: How can we use the solution to the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 to solve a real-world problem?

A: We can use the solution to the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 to solve a real-world problem by substituting different values of xx into the inequality and determining whether it is true or false. For example, we can use the solution to determine the number of hours that a person can work in a day to earn a certain amount of money.

Conclusion

In conclusion, we have answered some frequently asked questions related to the inequality 2x−1 \textless 102x - 1 \ \textless \ 10. We have discussed the solution to the inequality, how to write the solution in interval notation, and how to use the solution to solve a problem. We hope that this article has been helpful in answering your questions and has provided a clear understanding of the solution to the inequality.

Final Thoughts

In this article, we have discussed the inequality 2x−1 \textless 102x - 1 \ \textless \ 10 and answered some frequently asked questions related to the inequality. We have provided a clear understanding of the solution to the inequality and have discussed how to use the solution to solve a problem. We hope that this article has been helpful and has provided a valuable resource for students and teachers.

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