1MPES2 – Two-Step Equations Ecole Supérieure de Commerce de Neuchâtel Pierre Marchal 7.03.2016 http://creativecommons.org/licences/by/3.0/ Attribute to: Tyler Wallace (University of Memphis)
Objectives of the course By the end of the course, you should be able to: Do order of operations in reverse Addition and subtraction first Multiplication and division second Solve two-step equations
Two step equation When solving we do Order of Operations in First, we will and Then, we will and reverse add subtract multiply divide
ExampleS of Application
5 – 7x = 26 5 - 7x = 26 - 5 + 5 – 7x = 26 – 5 - 7 x = 21 – 5 Calculation ÷ - 7 Solution - 7 - 7 x = -3 Verification: 5 – 7 (-3) = 26 ✔ To do that we will focus on the negative 7 which is multiplied by x and the positive 5 which is added to the x. We know that we do order of operation in reverse, so we must start with the adding and subtracting. So let us focus on 5, to get rid of the 5, as it is a positive 5, we need to subtract 5. Just as always, if we subtract 5 on the left, we subtract 5 on the right. Now, the 5s subtract out to zero, and all that remains on the left side is negative 7 x equals 21. Remember that because there is nothing between the negative 7 and the x, that implies the operation is the multiplication. So to get the x alone, we must do the opposite of the multiplying, which is dividing out negative 7. Doing the same thing to the other side, we notice that the negative 7s divide out. We are left with x equals 21 divided by negative 7 which is negative 3. Notice, the negative 3 is the number that we can plug in for x to make this equation true. Negative 7 times negative 3 is positive 21, and 5 more is 26. Let us try another example.
14 = -2 + 4x 14 = -2 + 4 x 14 + 2 = 2 - 2 + 4x 16 = 4x + 2 Calculation ÷ 4 Solution 4 4 4 = x Verification: 14 = -2 + 4(4) ✔ The opposite of a negative 2 is a positive 2. And if we add 2 on the right side, we also must ad 2 on the left side. Notice the 2s subtract out to zero and all that remains on the right side is the 4 x. On the left side 14 + 2 is 16. Now to get the x alone, right now we have 4 x, the opposite of multiplying is dividing. To get rid of the 4 and to get x alone we divide by 4, on both sides. The 4s divide out, and we are left with x = 16 fourth or 4. Again, notice the 4 is the number that makes this equation works. Replace the x by 4, we have 4 times 4 equals 16, minus 2 equals 14. First we add and subtract , then we multiply or dive to get the x alone.
Practical exercises Ouvrez un de vos exemples précédent (pas votre sites) avec Notepad+ Insérer le code de l’exemple dans la partie <head> Sauvez sous « essai10.htm » Dans l’explorer double cliquez sur « essai10.htm » et observez le résultat.
First Second Third Fourth 2x + 3 = 15 6x – 3 = 15 6 + 3x = 15 3 + 5x = 18 -3 + 3x = 18 4 – 3x = 22 12 = 3x - 3 12 = 5x -3 - 8 = 3x + 4 25 = 9 + 4x 25 = -10 + 7x 20 = 10x - 5 x = 6 x = 3 x = 3 x = 45 x = 3 x = 7 x = - 6 x = 5 x = 5 x = 3 x = - 4 x = - 36 x = 4 x = 5 x = 2.5 x = 12
By the end of this course You are able to : Do order of operations in reverse: Addition and subtraction first Multiplication and division second Solve two-step equations
Any question ?
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