Solve The Inequality H 4 ≤ 5 \frac{h}{4} \leq 5 4 H ​ ≤ 5 . Graph The Solution On The Number Line.Drag Points To Select A Range, And Click Points To Mark As Open Or Closed.

Introduction

Inequalities are mathematical statements that compare two expressions using greater than, less than, greater than or equal to, or less than or equal to. Solving inequalities involves finding the values of the variable that make the inequality true. In this article, we will focus on solving the inequality $\frac{h}{4} \leq 5$ and graphing the solution on the number line.

Understanding the Inequality

The given inequality is $\frac{h}{4} \leq 5$. This means that the value of $h$ divided by 4 is less than or equal to 5. To solve this inequality, we need to isolate the variable $h$.

Step 1: Multiply Both Sides by 4

To isolate $h$, we can multiply both sides of the inequality by 4. This will cancel out the fraction and give us the value of $h$.

\frac{h}{4} \leq 5

Multiplying both sides by 4 gives us:

h \leq 20

Step 2: Write the Solution in Interval Notation

The solution to the inequality is $h \leq 20$. This means that the value of $h$ can be any real number less than or equal to 20. We can write this in interval notation as $(-\infty, 20]$.

Graphing the Solution on the Number Line

To graph the solution on the number line, we need to mark the point 20 as closed and all points to the left of 20 as shaded.

(-\infty, 20]

Conclusion

In this article, we solved the inequality $\frac{h}{4} \leq 5$ and graphed the solution on the number line. We used the steps of multiplying both sides by 4 and writing the solution in interval notation to find the solution. We also graphed the solution on the number line by marking the point 20 as closed and all points to the left of 20 as shaded.

Tips and Tricks

• When solving inequalities, always remember to multiply both sides by the same value to keep the inequality true.
• When graphing the solution on the number line, make sure to mark the point as closed or open depending on whether it is included in the solution or not.
• When writing the solution in interval notation, make sure to use the correct notation to represent the solution.

Common Mistakes to Avoid

• When solving inequalities, do not forget to multiply both sides by the same value to keep the inequality true.
• When graphing the solution on the number line, do not forget to mark the point as closed or open depending on whether it is included in the solution or not.
• When writing the solution in interval notation, do not forget to use the correct notation to represent the solution.

Real-World Applications

Solving inequalities has many real-world applications. For example, in finance, inequalities can be used to determine the minimum or maximum value of an investment. In engineering, inequalities can be used to determine the minimum or maximum value of a physical quantity such as temperature or pressure.

Practice Problems

1. Solve the inequality $\frac{x}{3} \geq 2$ and graph the solution on the number line.
2. Solve the inequality $x - 2 \leq 5$ and graph the solution on the number line.
3. Solve the inequality $\frac{y}{2} \leq 3$ and graph the solution on the number line.

Answer Key

1. $x \geq 6$
2. $x \leq 7$
3. $y \leq 6$

Conclusion

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Introduction

In our previous article, we solved the inequality $\frac{h}{4} \leq 5$ and graphed the solution on the number line. In this article, we will provide a Q&A guide to help you better understand how to solve inequalities and graph the solution on the number line.

Q: What is an inequality?

A: An inequality is a mathematical statement that compares two expressions using greater than, less than, greater than or equal to, or less than or equal to.

Q: How do I solve an inequality?

A: To solve an inequality, you need to isolate the variable by performing the same operation on both sides of the inequality.

Q: What are the steps to solve an inequality?

A: The steps to solve an inequality are:

1. Multiply both sides of the inequality by the same value to keep the inequality true.
2. Add or subtract the same value from both sides of the inequality to isolate the variable.
3. Write the solution in interval notation.

Q: How do I graph the solution on the number line?

A: To graph the solution on the number line, you need to mark the point as closed or open depending on whether it is included in the solution or not.

Q: What is interval notation?

A: Interval notation is a way of writing the solution to an inequality using a specific notation.

Q: How do I write the solution in interval notation?

A: To write the solution in interval notation, you need to use the following notation:

• $(-\infty, a)$ to represent all real numbers less than $a$
• $(a, \infty)$ to represent all real numbers greater than $a$
• $(-\infty, a]$ to represent all real numbers less than or equal to $a$
• $[a, \infty)$ to represent all real numbers greater than or equal to $a$

Q: What are some common mistakes to avoid when solving inequalities?

A: Some common mistakes to avoid when solving inequalities are:

• Forgetting to multiply both sides of the inequality by the same value
• Forgetting to add or subtract the same value from both sides of the inequality
• Writing the solution in interval notation incorrectly

Q: How do I determine if a point is included in the solution or not?

A: To determine if a point is included in the solution or not, you need to check if the point is less than or equal to the value of the variable.

Q: What are some real-world applications of solving inequalities?

A: Some real-world applications of solving inequalities include:

• Finance: Inequalities can be used to determine the minimum or maximum value of an investment.
• Engineering: Inequalities can be used to determine the minimum or maximum value of a physical quantity such as temperature or pressure.

Q: How do I practice solving inequalities?

A: To practice solving inequalities, you can try solving the following problems:

1. Solve the inequality $\frac{x}{3} \geq 2$ and graph the solution on the number line.
2. Solve the inequality $x - 2 \leq 5$ and graph the solution on the number line.
3. Solve the inequality $\frac{y}{2} \leq 3$ and graph the solution on the number line.

Answer Key

1. $x \geq 6$
2. $x \leq 7$
3. $y \leq 6$

Conclusion

In this article, we provided a Q&A guide to help you better understand how to solve inequalities and graph the solution on the number line. We hope that this article has provided you with a better understanding of how to solve inequalities and graph the solution on the number line.