1. 1MPES2 – Equations Ecole Supérieure de Commerce de Neuchâtel Pierre Marchal 22.02.2016 http://creativecommons.org/licences/by/3.0/ Attribute to: Tyler Wallace (University of Memphis)

2. Objectives of the course By the end of the course, you should be able to: – Give the definition of an equation – Give some examples – Give the form of an equation of the 1 st degree – Give the definition of the degree of an equation

3. DEFINITION OF AN EQUATION

4. Definition An equation is whose two parts are 3x + 5 = 12 Left part Right part an equality polynomials

5. Examples 3x + 125 = 2 a 2 - 2a - 7 = 2a + 2 5x + y = 18 – x 5x + 3 y + 15 = 0 …

6. Practical exercise

7. Is it an equation or not ? 2x + 5 = 7 3u = 0 2y + 5 = 7 = 17y - 2 2v + 3 = 7w – 8 5z + 4 – 2 9 = w – 17 5 = 5 ☐☐☐☐☐☐☐ ✔ ✔ ✔ ✔ ✔ ✔ ✔ YESNO

8. DEGREE OF AN EQUATION

9. Degree of an equation The degree of an equation is the degree of the in the 2 parts (left part and right part) Any equation of the can be written in the following form: o ax + b = 0 (with a ≠ 0) polynomial of higher degree first degree

10. EXAMPLE OF APPLICATION

11. What degree? 2x + 5 = 7 2x 3 + 5 = 0 2x + 5 = 7x 2 - 3x + 1 5 = 7 – 2 y = 7x 2 + x – 13 y 2 = x 2 - 13 5 = 5 1 DEGREE 3 2 0 2 1 1

12. SOLVING AN EQUATION

13. Solving an equation Is finding that makes the equation A mandatory step after solving an equation is To do that: – Replace the variable by the – And check that true checking the solution solution the equation is true the value(s) of the variables(s)

14. STRATEGIES SOLVING EQUATIONS

15. Strategies for 1 st degree equations In the coming courses we’ll solve: – equations – Equations with – One-step Two-step General fractions distribution Formulas

16. By the end of this course You are able to : – Give the definition of an equation – Provide some examples – Give the form of an equation of the 1 st degree – Give the definition of the degree of an equation

17. Any question ?

18. THANK YOU FOR YOUR ATTENTION See you on Thursday, and please, learn your lesson !