Which Choice Is The Solution To The Inequality Below? 2 X \textless 30 2x \ \textless \ 30 2 X \textless 30 A. X \textless 30 X \ \textless \ 30 X \textless 30 B. X \textless 15 X \ \textless \ 15 X \textless 15 C. X \textgreater 30 X \ \textgreater \ 30 X \textgreater 30 D. X \textgreater 15 X \ \textgreater \ 15 X \textgreater 15

Understanding the Inequality

When dealing with inequalities, it's essential to understand the relationship between the variables and the constants involved. In this case, we have the inequality $2x < 30$. To solve for $x$, we need to isolate the variable on one side of the inequality sign.

Isolating the Variable

To isolate $x$, we can divide both sides of the inequality by 2. This will give us the value of $x$ that satisfies the inequality. When we divide both sides by 2, we get:

$$\frac{2x}{2} < \frac{30}{2}$$

Simplifying the expression, we get:

$$x < 15$$

Analyzing the Choices

Now that we have the solution to the inequality, let's analyze the choices given:

A. $x < 30$ B. $x < 15$ C. $x > 30$ D. $x > 15$

Evaluating Choice A

Choice A states that $x < 30$. However, this is not the solution to the inequality $2x < 30$. If we substitute $x = 30$ into the original inequality, we get $2(30) < 30$, which is not true. Therefore, choice A is not the solution to the inequality.

Evaluating Choice B

Choice B states that $x < 15$. This is the solution to the inequality $2x < 30$. If we substitute $x = 15$ into the original inequality, we get $2(15) < 30$, which is true. Therefore, choice B is the solution to the inequality.

Evaluating Choice C

Choice C states that $x > 30$. However, this is not the solution to the inequality $2x < 30$. If we substitute $x = 30$ into the original inequality, we get $2(30) < 30$, which is not true. Therefore, choice C is not the solution to the inequality.

Evaluating Choice D

Choice D states that $x > 15$. However, this is not the solution to the inequality $2x < 30$. If we substitute $x = 15$ into the original inequality, we get $2(15) < 30$, which is true. However, if we substitute $x = 16$ into the original inequality, we get $2(16) < 30$, which is also true. Therefore, choice D is not the solution to the inequality.

Conclusion

In conclusion, the solution to the inequality $2x < 30$ is $x < 15$. Therefore, the correct choice is:

• The final answer is B.
  

Understanding Inequalities

Inequalities are mathematical statements that compare two expressions, indicating whether they are equal, greater than, or less than each other. Inequalities are used to describe relationships between variables and constants, and they play a crucial role in solving problems in mathematics, science, and engineering.

Q&A

Q: What is an inequality?

A: An inequality is a mathematical statement that compares two expressions, indicating whether they are equal, greater than, or less than each other.

Q: What are the different types of inequalities?

A: There are three main types of inequalities:

• Linear inequalities: These are inequalities that involve a linear expression, such as $2x < 30$.
• Quadratic inequalities: These are inequalities that involve a quadratic expression, such as $x^2 + 4x + 4 > 0$.
• Absolute value inequalities: These are inequalities that involve an absolute value expression, such as $|x| < 3$.

Q: How do I solve a linear inequality?

A: To solve a linear inequality, you can follow these steps:

1. Isolate the variable: Move all the terms with the variable to one side of the inequality sign.
2. Simplify the expression: Simplify the expression on the other side of the inequality sign.
3. Write the solution: Write the solution in interval notation, such as $x < 15$.

Q: How do I solve a quadratic inequality?

A: To solve a quadratic inequality, you can follow these steps:

1. Factor the quadratic expression: Factor the quadratic expression, if possible.
2. Find the roots: Find the roots of the quadratic expression.
3. Determine the sign: Determine the sign of the quadratic expression between the roots.
4. Write the solution: Write the solution in interval notation, such as $x < -2$ or $x > 3$.

Q: How do I solve an absolute value inequality?

A: To solve an absolute value inequality, you can follow these steps:

1. Write two inequalities: Write two inequalities, one for the positive case and one for the negative case.
2. Solve each inequality: Solve each inequality separately.
3. Combine the solutions: Combine the solutions to get the final answer.

Q: What is the difference between an inequality and an equation?

A: An inequality is a mathematical statement that compares two expressions, indicating whether they are equal, greater than, or less than each other. An equation is a mathematical statement that states that two expressions are equal.

Q: Can I use algebraic manipulations to solve an inequality?

A: Yes, you can use algebraic manipulations to solve an inequality. However, you must be careful not to change the direction of the inequality sign.

Q: Can I use a calculator to solve an inequality?

A: Yes, you can use a calculator to solve an inequality. However, you must be careful to enter the correct values and to interpret the results correctly.

Conclusion

In conclusion, inequalities are an essential part of mathematics, and solving them requires a clear understanding of the concepts and techniques involved. By following the steps outlined in this article, you can solve a wide range of inequalities and apply them to real-world problems.

Additional Resources

• Inequality solver: A calculator or online tool that can solve inequalities.
• Inequality examples: A collection of examples and exercises that illustrate the concepts and techniques involved in solving inequalities.
• Inequality tutorials: A series of tutorials that provide step-by-step instructions and explanations for solving inequalities.

Final Thoughts

Solving inequalities requires a combination of mathematical knowledge, problem-solving skills, and critical thinking. By practicing and applying the concepts and techniques outlined in this article, you can become proficient in solving inequalities and apply them to a wide range of real-world problems.