Solving and Graphing Linear Inequalities By: Luisa Sanchez, Sophia Rodriguez, and Ximena Carabaza

Important Vocabulary/signs Inequality- a number sentence where one side is not necessarily equal to the other side. There are several possible answers that will make an inequality true statement Solution of an inequality- any number that makes an inequality true. Equivalent inequalities- inequalities with the solution Compound inequalities- two inequalities that are joined by the word “and” or the word “or”

Solving Inequalities When we solve inequalities we have to get the variables defined. WHAT WE DO TO ONE SIDE, WE DO TO THE OTHER Your goal is to have the variable on one side; and the number on the other side of the inequality sign Tips The inequality sign is like an equal sign Treat this like an equation and SIMPLIFY!!!!!!!

The Basics A < B A is less than B or the left side is less than the right side A < B A is less than or equal to B or the left is less than or equal to the right Your X CANNOT BE NEGATIVE If it is, divide by -1 and your signs will change

Open Circles When your answer looks something like this: x>2, your answer literally reads, x is greater than 2. There is no line under the “greater than” sign, so when you graph, you will have an open circle. That is because x is strictly greater than two, if you plug in any number greater than two, the inequality will be true.

Closed Circles When you have something like this: x>10, as your final answer, your answer literally reads x is greater than or equal to 10. Meaning that when you graph you will have a “closed circle” because, 10 or any number greater than 10 would make the inequality true.

Example 1 X-3<5 Step 1- solve like an equation Notice that there is no line under the “less than” symbol so if we would have to graph this, this would be an open circle. Note: If the variable comes first in the inequality, when you graph you can think of the sign as an arrow and shade your graph in the direction the sign is pointing to. X<8 is your final answer

Example 2 11<x-4 Step 1- solve like an equation Your answer is 15<x

Graphing After solving your inequalities the next step is to graph Follow the following steps: Step 1- draw a number line with the correct numbers Step 2- determine whether it is opened or closed circle Step 3- shade in the correct direction Remember your X CANNOT BE NEGATIVE!!!!!!!!!

How to turn a graph into an inequality Step 1: Pick a variable Step 2: Define the variable Step 3: Determine if you have an open or closed circle Step 4: Determine if you have a “less than” or “greater than” sign Step 5: write the inequality

Example 1 Equation- X>-5 Step 1- draw a number line with the correct numbers Step 2- determine whether it is opened or closed circle Step 3- shade in the correct direction

Example 2 -2 < x Step 1- draw a number line with the correct numbers Step 2- determine whether it is opened or closed circle Step 3- shade in the correct direction

Example 3 x > 1 Step 1- draw a number line with the correct numbers Step 2- determine whether it is opened or closed circle Step 3- shade in the correct direction

Time for Practice To make sure you understand what we just taught or for further points of clarification. We are going to play a game.

1 solve and graph X-5 < 15

2 16>y-7

3 Make an equation

4 10-L> 15

5 X-9 < 5

6 M-11<19

7 Make an equation