Question

1. # Which Of The Following Is The Correct Graph Of The Solution To The Inequality −13 > −5X + 2 > −28?

Understanding how to graph an inequality is a crucial part of algebra. It’s important to be able to represent the solution in a graphical form. Graphs can give us an immediate visual understanding of the relationship between variables, which can help us understand complex problems more quickly and easily. In this blog post, we will discuss the steps for graphing the solution to an inequality such as −13 > −5x + 2 > −28. We’ll also discuss why it’s important to understand how to graph inequalities and how it can help us solve real-world problems.

## What is an inequality?

An inequality is a statement that two values are not equal. In mathematics, inequalities are usually represented by one of the following symbols: < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

For example, the statement “x is less than y” can be represented as: x < y

## What is a graph?

A graph is a visual representation of data. It can be used to represent a function, a set of data points, or a relationship between two variables. Graphs can be created by hand or with a computer program.

## The different types of graphs

There are four different types of graphs that can be used to represent the solution to an inequality: circle, line, shading, and sign.

1. The Circle Graph: A circle graph is used when the solution to an inequality is all real numbers. The inequality is represented by a circle with the symbol “<” or “>” inside of it.

2. The Line Graph: A line graph is used when the solution to an inequality is a set of points on a line. The inequality is represented by a line with the symbol “<” or “>” next to it.

3. The Shading Graph: A shading graph is used when the solution to an inequality is a region of space. The inequality is represented by shading in the appropriate region with the symbol “<” or “>” next to it.

4. The Sign Graph: A sign graph is used when the solution to an inequality is one or more specific values. The inequality is represented by placing the symbols “<” or “>” next to those specific values.

## How to graph an inequality

There are a few steps that you need to follow in order to graph the inequality correctly. First, you need to find the y-intercept which is the point where the line crosses the y-axis. To do this, you need to set x=0 in the equation and solve for y. In this case, the y-intercept would be (0,-3). Next, you need to find the x-intercept which is the point where the line crosses the x-axis. To do this, you set y=0 in the equation and solve for x. In this case, the x-intercept would be (2,0). Lastly, you need to determine which way the inequality goes. You can do this by plugging in a point that is not on either axis such as (1,-2) into the inequality. If it works out, then that is your solution set. If not, then you need to flip the inequality around. In this case, you would get > -x + 3> -1 which would give you your solution set of all points that satisfy > -x + 3> -1

## Practice problems

Assuming you are talking about the graph of the solutions to the inequality:

The correct graph would be a number line with a closed circle at -3 and an open circle at 5. This means that all numbers greater than -3 and less than 5 (exclusive) satisfy the inequality.

## Conclusion

In this article, we explored the correct graph of the solution to the inequality −13 > −5X + 2 > −28. We learned that it was represented by a number line with two open circles at -2 and 5, and a solid circle in between them at 0. This is an important concept to understand when solving inequalities and graphing their solutions. Now that you have mastered this skill, you are ready to try more advanced equations!

2. Are you trying to figure out the correct graph of the solution to the inequality -13 > -5X + 2 > -28? Don’t worry, you’re not alone! Plotting inequalities can be tricky, but with the right steps, you can do it with ease.

First, let’s break the inequality into separate parts: -13 > -5X + 2 and -5X + 2 > -28. To graph the first part, we need to plot two points. We know that -13 is greater than -5X + 2, so our points should be above the line. Since -5X + 2 = -13 when X = 0, let’s plot (0, -13). To find our second point, let’s solve for X when -5X + 2 = -28. Subtract 2 from both sides, and divide both sides by -5. This gives us X = 4. Now, let’s plot (4, -28).

Next, let’s graph the second part of the inequality, -5X + 2 > -28. We know that -5X + 2 is greater than -28 when X = 0, so let’s plot (0, -28). To find our second point, let’s solve for X when -5X + 2 = -13. We can do this by subtracting 2 from both sides, and dividing both sides by -5. This gives us X = 2. Now, let’s plot (2, -13).

Now that we have the two parts of the inequality plotted out, we can draw the graph of the solution. We can see that the solution is all the x-values between 0 and 4, and all the y-values between -28 and -13. This gives us a shaded region in the first quadrant, as shown below:

So, there we have it! The correct graph of the solution to the inequality -13 > -5X + 2 > -28 is a shaded region in the first quadrant.

We hope this blog post has helped you understand how to graph solutions to inequalities. Now you can confidently plot these solutions with ease. Best of luck!