# Graphing Solutions to Linear Inequalities | Math

November 5, 2014
Many of the components you’ve been studying for the TASC Test Assessing Secondary Completion™ Mathematics subtest are related. For example, the terms you learned when you reviewed equations will help you understand linear inequalities as well. Math builds on itself. The more you know, the more you’ll understand. Though you should keep practicing the skills that you’ve studied, such as equations, you can start to apply your knowledge to solving and graphing linear inequalities. First thing’s first: what is a linear inequality?

## Linear Inequalities

An inequality  simply means that the equation is not equal. You know that one side of the equation is larger than the other. Inequalities are often indicated with greater than (>) or less than (<) signs. For example: 6 > 2 3 < 50 You may also see a line underneath the greater than sign (≥) or the less than sign (≤), which means that the sides of the equation are either greater than or equal to, or less than or equal to, respectively. You might be asked to solve, or simplify, an inequality. You would treat it like an equation. For example: x + 4 > 24 x + 4 (- 4) > 24 (- 4) x > 20 You might be asked to illustrate or identify a linear inequality on a line. To do this for the previous example, you would create your line:   Map the inequality onto the line by circling the dash that indicates the starting point (in this case, 20), and drawing a line towards the right (if it’s greater than) or the left (if it’s less than). When your inequality is greater than or less than, the circle is hollow. When it’s greater than or equal to, or less than or equal to, the circle is solid (filled in):

## How to Graph Solutions

To graph the solutions to linear inequalities, the first step is to simplify the equation. For example: 2x + 4 > y + 8 2x + 4 (- 4) > y + 8 (- 4) 2x > y + 4 When graphing, you want the y variable on the left and everything else on the right. So, you have to rearrange the equation: 2x > y + 4 y + 4 < 2x y + 4 (- 4) < 2x (- 4) y < 2x – 4 Once your equation is set up correctly, follow these steps:
1. Draw your line, starting at the y axis where your constant is (using the operator, the addition sign or subtraction sign, to decide whether the line should start in the positive or negative, respectively) and running through the coefficient.
2. Plot the y=. If your inequality is > or <, you’ll use a dashed line. If it’s ≥ or ≤, you’ll use a solid line.
3. Shade the graph, above the line for greater than (and greater than or equal to) and below the line for less than (and less than or equal to).
Our previous example, then, would be graphed this way:
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