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. AlgebraSolutions of Equations and InequalitiesBy: Mr. Schwark

2. Solve for a Variable A variable represents a numberWe do not know the numberX will be the variableWe will solve for X

3. Equation Form2X + 4 = 10X – 3 = 75X – 10 = 20 – 5X

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

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

6. Basic RulesGet X by itselfNote: If you preform an operation to one side, you also must preform the same operation to the other side.

7. Lets Try ExamplesEx 13X + 5 = 20 -5 -5 3X = 15 ÷3 ÷3 X = 5Ex 21/2X – 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 = 20Ex 2½(20) – 10 = 0 10 – 10 = 0 0 = 0

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

10. Examples of InequalitiesX + 3 < 52X – 6 > 84X + 2 < 10-6X – 10 > 20

11. Solve for InequalitySolve same as EquationGet X by itselfX = ?

12. Rules of InequalitiesSame rules as equationsWith one exception:When dividing by a negative you must switch the direction of the sign.

13. Lets Try ExamplesEx 1-2X – 10 < 4 +10 +10 -2X < 14 ÷(-2) ÷(-2) X > -7Ex 23X + 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 GraphX > -2X < -1X < 0X > 1

16. CitationsAll GraphsSchwark, Adam. Sept. 27 2011, creative commons