This document discusses solving equations and inequalities for a variable. It explains that a variable represents an unknown number and the goal is to isolate the variable on one side of the equation or inequality symbol. The basic steps are to use addition, subtraction, multiplication, and division to manipulate the equation or inequality until the variable is alone. Examples are provided and checked by plugging solutions back into the original expressions. Inequalities follow the same process but with different symbols (<, >, ≤, ≥) to indicate relationships and a rule for dividing by a negative number is given. Finally, inequalities are graphed on a number line.

1. Algebra Solutions of Equations and Inequalities By: Mr. Schwark

2. Solve for a Variable A variable represents a number We do not know the number X will be the variable We will solve for X

3. Equation Form 2X + 4 = 10 X – 3 = 7 5X – 10 = 20 – 5X

4. Solve for X Get X by itself - Get X on only one side X = ?

5. How to Get X Alone - Use Basic Math to Solve (−) Subtract (+) Add (x) Multiply (÷) Divide

6. Basic Rules Get X by itself Note: If you preform an operation to one side, you also must preform the same operation to the other side.

7. Lets Try Examples Ex 1 3X + 5 = 20 -5 -5 3X = 15 ÷3 ÷3 X = 5 Ex 2 1/2X – 10 = 0 +10 +10 1/2X = 10 x2 x2 X = 20

8. Check the Answers - Plug in your value for X - Ex 1 3(5) + 5 = 20 15 + 5 = 20 20 = 20 Ex 2 ½(20) – 10 = 0 10 – 10 = 0 0 = 0

9. Solve for Inequalities What is an Inequalities < Less then > Greater then < Less then or equal to > Greater then or equal to

10. Examples of Inequalities X + 3 < 5 2X – 6 > 8 4X + 2 < 10 -6X – 10 > 20

11. Solve for Inequality Solve same as Equation Get X by itself X = ?

12. Rules of Inequalities Same rules as equations With one exception: When dividing by a negative you must switch the direction of the sign.

13. Lets Try Examples Ex 1 -2X – 10 < 4 +10 +10 -2X < 14 ÷(-2) ÷(-2) X > -7 Ex 2 3X + 15 > 9 -15 -15 3X > -6 ÷3÷3 X > -2

14. Graph an Inequality < = ) Less then > = ( Greater then < = ] Less then or equal >= [ Grater then or equal

15. Examples of Graph X > -2 X < -1 X < 0 X > 1

16. Citations All Graphs Schwark, Adam. Sept. 27 2011, creative commons