Consider The Following Inequality:$-\frac{n}{3.5} \ \textgreater \ -1$1. Solve The Inequality For $n$.2. Graph The Solution.

Solving and Graphing the Inequality: A Step-by-Step Guide

In this article, we will explore the process of solving and graphing the given inequality: $-\frac{n}{3.5} \ \textgreater \ -1$. We will break down the solution into manageable steps, making it easy to understand and follow along. By the end of this article, you will have a clear understanding of how to solve and graph this type of inequality.

Step 1: Multiply Both Sides by -3.5

To solve the inequality, we need to isolate the variable $n$. The first step is to multiply both sides of the inequality by $-3.5$. This will eliminate the fraction and make it easier to work with.

$-\frac{n}{3.5} \ \textgreater \ -1$

$-n \ \textgreater \ -3.5 \times -1$

$-n \ \textgreater \ 3.5$

Step 2: Multiply Both Sides by -1

To make the inequality easier to read, we can multiply both sides by $-1$. This will change the direction of the inequality sign.

$-n \ \textgreater \ 3.5$

$n \ \textless \ -3.5$

Step 3: Write the Solution in Interval Notation

Now that we have isolated the variable $n$, we can write the solution in interval notation. The solution is all real numbers less than $-3.5$.

$(-\infty, -3.5)$

Graphing the Solution

To graph the solution, we can use a number line. We will plot a point at $-3.5$ and shade the region to the left of the point.

Graph of the Solution

The graph of the solution is a line segment on the number line, extending from negative infinity to $-3.5$.

In this article, we solved and graphed the inequality $-\frac{n}{3.5} \ \textgreater \ -1$. We broke down the solution into manageable steps, making it easy to understand and follow along. By the end of this article, you should have a clear understanding of how to solve and graph this type of inequality.

Key Takeaways

• To solve the inequality, we need to isolate the variable $n$.
• We can multiply both sides of the inequality by $-3.5$ to eliminate the fraction.
• We can multiply both sides of the inequality by $-1$ to make the inequality easier to read.
• The solution is all real numbers less than $-3.5$.
• We can graph the solution using a number line.

Final Thoughts

Solving and graphing inequalities is an important skill in mathematics. By following the steps outlined in this article, you can solve and graph inequalities with ease. Remember to always isolate the variable, multiply both sides by the same value, and write the solution in interval notation. With practice, you will become proficient in solving and graphing inequalities.
Frequently Asked Questions: Solving and Graphing Inequalities

In our previous article, we explored the process of solving and graphing the inequality $-\frac{n}{3.5} \ \textgreater \ -1$. We broke down the solution into manageable steps, making it easy to understand and follow along. In this article, we will answer some of the most frequently asked questions about solving and graphing inequalities.

Q: What is the first step in solving an inequality?

A: The first step in solving an inequality is to isolate the variable. This means getting the variable by itself on one side of the inequality sign.

Q: How do I know which direction to shade the region on the number line?

A: To determine which direction to shade the region, you need to look at the inequality sign. If the inequality sign is greater than (>) or less than (<), you will shade the region to the right or left of the point, respectively.

Q: Can I multiply both sides of the inequality by a negative number?

A: Yes, you can multiply both sides of the inequality by a negative number. However, you need to be careful when doing so, as it will change the direction of the inequality sign.

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

A: To write the solution in interval notation, you need to use the following format: $(a, b)$. The $a$ represents the lower bound of the interval, and the $b$ represents the upper bound.

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, on the other hand, 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: Can I use a calculator to solve an inequality?

A: Yes, you can use a calculator to solve an inequality. However, you need to be careful when using a calculator, as it may not always give you the correct solution.

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

A: To graph an inequality on a number line, you need to plot a point at the value of the variable, and then shade the region to the left or right of the point, depending on the direction of the inequality sign.

Q: What is the importance of solving and graphing inequalities?

A: Solving and graphing inequalities is an important skill in mathematics, as it allows you to solve real-world problems and make informed decisions. Inequalities are used in a wide range of fields, including business, economics, and science.

In this article, we answered some of the most frequently asked questions about solving and graphing inequalities. We hope that this article has been helpful in clarifying any confusion you may have had about solving and graphing inequalities. Remember to always isolate the variable, multiply both sides by the same value, and write the solution in interval notation. With practice, you will become proficient in solving and graphing inequalities.