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math

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  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 < -1 X > -2 X < 0 X > 1

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

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