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