Graph The Solution Of This Inequality:$4.5x - 100 \ \textgreater \ 125$Drag A Point To The Number Line.

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Introduction

In mathematics, inequalities are a fundamental concept that plays a crucial role in solving various problems. An inequality is a statement that two expressions are not equal, but one is greater than or less than the other. In this article, we will focus on solving the inequality $4.5x - 100 > 125$ and graphing its solution on a number line.

Understanding the Inequality

The given inequality is $4.5x - 100 > 125$. To solve this inequality, we need to isolate the variable $x$ on one side of the inequality sign. We can start by adding $100$ to both sides of the inequality, which gives us:

$$4.5x > 225$$

Adding 100 to Both Sides

By adding $100$ to both sides of the inequality, we have effectively eliminated the constant term $-100$ from the left-hand side of the inequality. This step is essential in isolating the variable $x$.

Dividing Both Sides by 4.5

To isolate the variable $x$, we need to divide both sides of the inequality by $4.5$. This will give us:

$$x > \frac{225}{4.5}$$

Simplifying the Right-Hand Side

To simplify the right-hand side of the inequality, we can divide $225$ by $4.5$, which gives us:

$$x > 50$$

Graphing the Solution on a Number Line

Now that we have solved the inequality, we can graph its solution on a number line. To do this, we need to identify the point on the number line that corresponds to the value of $x$ that satisfies the inequality. In this case, the point on the number line that corresponds to $x = 50$ is the point $50$.

Dragging a Point to the Number Line

To graph the solution of the inequality on a number line, we can drag a point to the number line. The point should be placed at the value of $x$ that satisfies the inequality, which is $50$ in this case.

Conclusion

In conclusion, solving the inequality $4.5x - 100 > 125$ involves adding $100$ to both sides of the inequality, dividing both sides by $4.5$, and simplifying the right-hand side. The solution to the inequality is $x > 50$, which can be graphed on a number line by dragging a point to the number line at the value of $x$ that satisfies the inequality.

Frequently Asked Questions

• What is the solution to the inequality $4.5x - 100 > 125$?
• How do I graph the solution of the inequality on a number line?
• What is the value of $x$ that satisfies the inequality $4.5x - 100 > 125$?

Step-by-Step Solution

1. Add $100$ to both sides of the inequality: $4.5x - 100 + 100 > 125 + 100$
2. Simplify the left-hand side of the inequality: $4.5x > 225$
3. Divide both sides of the inequality by $4.5$: $\frac{4.5x}{4.5} > \frac{225}{4.5}$
4. Simplify the right-hand side of the inequality: $x > 50$

Graphing the Solution on a Number Line

To graph the solution of the inequality on a number line, follow these steps:

1. Identify the point on the number line that corresponds to the value of $x$ that satisfies the inequality.
2. Place a point on the number line at the value of $x$ that satisfies the inequality.
3. Draw an arrow on the number line to indicate that the solution extends to the right of the point.

Real-World Applications

Solving inequalities has numerous real-world applications in various fields, including:

• Business: Inequalities are used to model and solve problems related to profit, loss, and revenue.
• Economics: Inequalities are used to model and solve problems related to supply and demand, inflation, and unemployment.
• Science: Inequalities are used to model and solve problems related to population growth, chemical reactions, and physical systems.

Conclusion

In conclusion, solving the inequality $4.5x - 100 > 125$ involves adding $100$ to both sides of the inequality, dividing both sides by $4.5$, and simplifying the right-hand side. The solution to the inequality is $x > 50$, which can be graphed on a number line by dragging a point to the number line at the value of $x$ that satisfies the inequality.

Introduction

Solving inequalities is a fundamental concept in mathematics that has numerous real-world applications. In this article, we will address some of the most frequently asked questions related to solving inequalities.

Q: What is an inequality?

A: An inequality is a statement that two expressions are not equal, but one is greater than or less than the other. Inequalities are denoted by the use of the following symbols:

• Greater than: $>$
• Less than: $<$

Q: How do I solve an inequality?

A: To solve an inequality, you need to isolate the variable on one side of the inequality sign. This can be done by adding or subtracting the same value to both sides of the inequality, or by multiplying or dividing both sides of the inequality by the same non-zero value.

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

A: A linear inequality is an inequality that can be written in the form $ax + b > c$ or $ax + b < c$, where $a$, $b$, and $c$ are constants. A quadratic inequality is an inequality that can be written in the form $ax^2 + bx + c > 0$ or $ax^2 + bx + c < 0$, where $a$, $b$, and $c$ are constants.

Q: How do I graph the solution of an inequality on a number line?

A: To graph the solution of an inequality on a number line, you need to identify the point on the number line that corresponds to the value of the variable that satisfies the inequality. You then draw an arrow on the number line to indicate that the solution extends to the right or left of the point.

Q: What is the solution to the inequality $2x + 5 > 11$?

A: To solve the inequality $2x + 5 > 11$, you need to isolate the variable $x$ on one side of the inequality sign. This can be done by subtracting $5$ from both sides of the inequality, which gives you:

$$2x > 6$$

You then divide both sides of the inequality by $2$, which gives you:

$$x > 3$$

Q: What is the solution to the inequality $x^2 + 4x + 4 > 0$?

A: To solve the inequality $x^2 + 4x + 4 > 0$, you need to factor the left-hand side of the inequality, which gives you:

$$(x + 2)^2 > 0$$

Since the square of any real number is always non-negative, the inequality is true for all real values of $x$.

Q: How do I use inequalities in real-world applications?

A: Inequalities are used in a wide range of real-world applications, including:

• Business: Inequalities are used to model and solve problems related to profit, loss, and revenue.
• Economics: Inequalities are used to model and solve problems related to supply and demand, inflation, and unemployment.
• Science: Inequalities are used to model and solve problems related to population growth, chemical reactions, and physical systems.

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

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

• Not isolating the variable on one side of the inequality sign.
• Not checking the direction of the inequality sign.
• Not considering the domain of the variable.

Conclusion

In conclusion, solving inequalities is a fundamental concept in mathematics that has numerous real-world applications. By understanding the basics of solving inequalities, you can apply this knowledge to a wide range of problems in business, economics, science, and other fields.

Additional Resources

• Khan Academy: Solving Inequalities
• Mathway: Solving Inequalities
• Wolfram Alpha: Solving Inequalities

Frequently Asked Questions

• What is an inequality?
• How do I solve an inequality?
• What is the difference between a linear inequality and a quadratic inequality?
• How do I graph the solution of an inequality on a number line?
• What is the solution to the inequality $2x + 5 > 11$?
• What is the solution to the inequality $x^2 + 4x + 4 > 0$?
• How do I use inequalities in real-world applications?
• What are some common mistakes to avoid when solving inequalities?