Select The Values That Make The Inequality { -5x \ \textless \ -15$}$ True. Then Write An Equivalent Inequality In Terms Of { X$}$.Numbers Written In Order From Least To Greatest:-7, -2, 0, 2, 3, 4, 6, 8, 13

Mar 9, 2025 by ADMIN 210 views

**Solving Linear Inequalities: A Step-by-Step Guide**

Introduction

In this article, we will explore the concept of solving linear inequalities, focusing on the inequality ${-5x < -15}$ . We will learn how to isolate the variable x and write an equivalent inequality in terms of x. Additionally, we will discuss how to select the values that make the inequality true.

Understanding Linear Inequalities

A linear inequality is an inequality that can be written in the form of ax + b < c, where a, b, and c are constants, and x is the variable. In this case, the inequality is ${-5x < -15}$ . Our goal is to isolate the variable x and determine the values that make the inequality true.

Solving the Inequality

To solve the inequality, we need to isolate the variable x. We can do this by dividing both sides of the inequality by -5. However, we must be careful when dividing by a negative number, as it will change the direction of the inequality.

-5x < -15
x > 3

Equivalent Inequality

Now that we have isolated the variable x, we can write an equivalent inequality in terms of x. The equivalent inequality is x > 3.

Selecting Values

To determine the values that make the inequality true, we need to select the values from the given list that are greater than 3. The values that make the inequality true are:

Discussion

In this article, we learned how to solve linear inequalities by isolating the variable x and writing an equivalent inequality in terms of x. We also discussed how to select the values that make the inequality true. By following these steps, we can solve linear inequalities and determine the values that make them true.

Conclusion

In conclusion, solving linear inequalities requires isolating the variable x and writing an equivalent inequality in terms of x. By following these steps, we can determine the values that make the inequality true. In this article, we learned how to solve the inequality ${-5x < -15}$ and select the values that make it true.

Additional Examples

Here are some additional examples of linear inequalities:

2x + 3 < 5
x - 2 > 1
4x - 1 < 3

Solving the Inequalities

To solve these inequalities, we need to isolate the variable x. We can do this by adding or subtracting the same value to both sides of the inequality, or by multiplying or dividing both sides by the same non-zero value.

2x + 3 < 5
2x < 2
x < 1
x - 2 > 1
x > 3
4x - 1 < 3
4x < 4
x < 1

Conclusion

Final Thoughts

Q: What is a linear inequality?

A: A linear inequality is an inequality that can be written in the form of ax + b < c, where a, b, and c are constants, and x is the variable.

Q: How do I solve a linear inequality?

A: To solve a linear inequality, you need to isolate the variable x. You can do this by adding or subtracting the same value to both sides of the inequality, or by multiplying or dividing both sides by the same non-zero value.

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

A: A linear equation is an equation that can be written in the form of ax + b = c, where a, b, and c are constants, and x is the variable. A linear inequality, on the other hand, is an inequality that can be written in the form of ax + b < c, where a, b, and c are constants, and x is the variable.

Q: How do I determine the values that make a linear inequality true?

A: To determine the values that make a linear inequality true, you need to select the values from the given list that satisfy the inequality. For example, if the inequality is x > 3, you would select the values 4, 6, 8, and 13.

Q: What is the importance of solving linear inequalities?

A: Solving linear inequalities is an important concept in mathematics, and it has many real-world applications. By understanding how to solve linear inequalities, you can make informed decisions and solve problems in a variety of fields, including science, engineering, and economics.

Q: Can you provide some examples of linear inequalities?

A: Here are some examples of linear inequalities:

2x + 3 < 5
x - 2 > 1
4x - 1 < 3

Q: How do I solve these inequalities?

A: To solve these inequalities, you need to isolate the variable x. You can do this by adding or subtracting the same value to both sides of the inequality, or by multiplying or dividing both sides by the same non-zero value.

2x + 3 < 5
2x < 2
x < 1
x - 2 > 1
x > 3
4x - 1 < 3
4x < 4
x < 1

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, on the other hand, is an inequality that is written with a non-strict symbol, such as ≤ or ≥.

Q: Can you provide some examples of strict and non-strict inequalities?

A: Here are some examples of strict and non-strict inequalities:

Strict inequality: x > 3
Non-strict inequality: x ≥ 3

Q: How do I determine the values that make a strict inequality true?

A: To determine the values that make a strict inequality true, you need to select the values from the given list that satisfy the inequality. For example, if the inequality is x > 3, you would select the values 4, 6, 8, and 13.

Q: How do I determine the values that make a non-strict inequality true?

A: To determine the values that make a non-strict inequality true, you need to select the values from the given list that satisfy the inequality. For example, if the inequality is x ≥ 3, you would select the values 3, 4, 6, 8, and 13.

Conclusion

In conclusion, solving linear inequalities is an important concept in mathematics, and it has many real-world applications. By understanding how to solve linear inequalities, you can make informed decisions and solve problems in a variety of fields, including science, engineering, and economics.