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# Math (Algebra)

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### Math (Algebra)

1. 1. Algebra<br />Solutions of Equations and Inequalities<br />By: Mr. Schwark<br />
2. 2. Solve for a Variable <br />A variable represents a number<br />We do not know the number<br />X will be the variable<br />We will solve for X<br />
3. 3. Equation Form<br />2X + 4 = 10<br />X – 3 = 7<br />5X – 10 = 20 – 5X <br />
4. 4. Solve for X<br />Get X by itself<br />- Get X on only one side<br />X = ?<br />
5. 5. How to Get X Alone<br />- Use Basic Math to Solve<br />(−) Subtract<br />(+) Add<br />(x) Multiply <br />(÷) Divide <br />
6. 6. Basic Rules<br />Get X by itself<br />Note: If you preform an operation to one side, you also must preform the same operation to the other side.<br />
7. 7. Lets Try Examples<br />Ex 1<br />3X + 5 = 20<br /> -5 -5<br /> 3X = 15<br /> ÷3 ÷3<br /> X = 5<br />Ex 2<br />1/2X – 10 = 0<br /> +10 +10<br /> 1/2X = 10<br /> x2 x2 <br /> X = 20<br />
8. 8. Check the Answers <br />- Plug in your value for X -<br />Ex 1<br /> 3(5) + 5 = 20<br /> 15 + 5 = 20 <br /> 20 = 20<br />Ex 2<br />½(20) – 10 = 0<br /> 10 – 10 = 0<br /> 0 = 0<br />
9. 9. Solve for Inequalities<br />What is an Inequalities<br /> < Less then<br /> > Greater then<br />< Less then or equal to<br />> Greater then or equal to<br />
10. 10. Examples of Inequalities<br />X + 3 < 5<br />2X – 6 > 8<br />4X + 2 < 10<br />-6X – 10 > 20<br />
11. 11. Solve for Inequality<br />Solve same as Equation<br />Get X by itself<br />X = ?<br />
12. 12. Rules of Inequalities<br />Same rules as equations<br />With one exception:<br />When dividing by a negative you must switch the direction of the sign.<br />
13. 13. Lets Try Examples<br />Ex 1<br />-2X – 10 < 4<br /> +10 +10<br /> -2X < 14<br /> ÷(-2) ÷(-2)<br /> X > -7<br />Ex 2<br />3X + 15 > 9<br /> -15 -15<br /> 3X > -6<br /> ÷3÷3<br /> X > -2<br />
14. 14. Graph an Inequality<br />< = ) Less then<br />> = ( Greater then<br />< = ] Less then or equal<br />>= [ Grater then or equal<br />
15. 15. Examples of Graph<br />X > -2<br />X < -1<br />X < 0<br />X > 1<br />
16. 16. Citations<br />All Graphs<br />Schwark, Adam. Sept. 27 2011, creative commons<br />