How to Graph Inequalities

An inequality in an equation is a mathematical statement that compares two values using an inequality symbol, such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to

In this article, we will cover:

• How to Graph Inequalities
• Solved Examples
• FAQs

An inequality in an equation is a mathematical statement that compares two values using an inequality symbol, such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). Inequalities express a relationship between two expressions, such as x > 5, meaning that x is greater than 5.

Like an equation, inequality can be solved by isolating the variable on one side of the inequality. However, the solution to an inequality is not a single value, but a range of values that make the inequality true.

Examples of inequalities include:

• x > 5 (x is greater than 5)
• y < 10 (y is less than 10)
• z ≥ 3 (z is greater than or equal to 3)

You can also solve an inequality using the same operations as an equation, but you need to remember to flip the inequality symbol if you multiply or divide both sides by a negative number.

Example:

x + 3 > 7

x > 4 (subtract 3 from both sides of the inequality)

Another Example:

3x < 6

x < 2 (divide both sides by 3)

You can also graph the solution of an inequality on a number line, with a closed dot for “greater than or equal to” or “less than or equal to” and an open dot for “greater than” or “less than”

It is important to note that solving and graphing inequalities gives you the set of all the solutions that make the inequality true, rather than a single solution.

How to Graph Inequalities

Graphing inequalities is a way to show the solutions to inequality on a number line. The solution for linear inequalities in two variables is an ordered pair that is true for the inequality statement. Let us say if Px + Qy > R is a linear inequality where x and y are two variables, then an ordered pair (x, y) satisfying the statement will be the required solution. Here’s how you can graph inequalities for an 8th grader:

1. Start by drawing a number line. This is the line where you will graph the solutions to the inequality.

2. We have to simplify the given linear inequality in the same way as we do in the case of linear equations. Also, for linear inequalities in two variables, we need two test points(for x and y).

3. Next, choose a test point. A test point is a point on the number line that you will use to test whether the inequality is true or false. You can choose any point on the number line as a test point, but it’s often easiest to choose 0 or 1.

4. Plug the test point into the inequality and solve. If the test point makes the inequality true, then the point is shaded in. If the test point makes the inequality false, then the point is not shaded in.

5. Use the inequality symbol to determine whether to shade above or below or left or right of the line. For example, if the inequality is “x > 3,” then you would shade in all the points to the right of 3 on the number line. If the inequality is “x < 4,” then you would shade in all the points to the left of 4 on the number line. For “greater than or equal to” or “less than or equal to” inequality use a closed dot or solid line and for “greater than” or “less than” use an open dot or shaded line.

Here is an example of how to graph the inequality “x > 2”:

1. Draw a number line
2. Choose a test point, for example, x = 1
3. Plug the test point into the inequality, 1 > 2, which is false
4. Shade all the points to the right of 2, because x > 2 means “greater than”

Another example:

Graph the inequality “y ≤ -3”

1. Draw a number line
2. Choose a test point, for example, y = -4
3. Plug the test point into the inequality, -4 ≤ -3, which is true
4. Shade all the points the below -3, because y ≤ -3 means “less than or equal”

It’s important to remember that the solution of an inequality is the set of all the values that make the inequality true, not a single value like an equation.

Order of Operations FAQS

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