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Algebra Made Easy( er )

Algebra Made Easy( er ). By Mrs. Sinclair. Algebra? Balance? Say WHAT?. Question: “The triple of a number is 6. Can you guess what that number is?”. 2. Because you know that 3 times 2 equals 6. Using the “language” of mathematics, the QUESTION can be stated as:. 3x=6.

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Algebra Made Easy( er )

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  1. Algebra Made Easy(er) By Mrs. Sinclair

  2. Algebra? Balance? Say WHAT?

  3. Question: “The triple of a number is 6. Can you guess what that number is?”

  4. 2 Because you know that 3 times 2 equals 6.

  5. Using the “language” of mathematics, the QUESTION can be stated as: 3x=6 “The triple of a number is 6.” By the way, 3X is the same as 3 times x

  6. The sentence: "Can you guess what that number is?” in math 'language' is X = ?

  7. “X” is the unknown number we need to find out. Using the “language” of mathematics, the ANSWER can be stated as: X = 2 “The number is 2”

  8. Let’s start from the very beginning. Looking at the equation, we don’t know the value of ‘x’ but we know one important thing: The LEFT side is EQUAL to the RIGHT side, and we have to believe this and move on with our lives.

  9. 3x – 4 = 7 + 2x this side is equal to this side

  10. Now we arrive at the first confusion about equations: Both sides are equal “in value” only, not the way they look in the paper. This is similar to stating: 2 + 3 = 5 This side is equal to this side

  11. Very easy to believe because you know that 2 plus 3 = 5, even if 2 + 3 is written differently than the number 5. The ‘=’ sign is saying both sides are equal in value not in appearance. So, when you get an equation to solve, you start by believing that the equal sign is telling the absolute truth: both sides are equal in value.

  12. Our main goal : The 'x' by its own

  13. Let’s say we were given this statement x + 7 How can we get rid of the 7 so we keep only the x? The x is being added 7 units so we make just the opposite: we subtract 7 units. x + 7 - 7 Because 7 – 7 is equal to zero both sevens disappear. The x alone.

  14. Let’s say we were given this statement X - 2 How can we get rid of the -2 so we keep only the x? The x is being subtracted 2 units so we make just the opposite: we add 2 units. X – 2+2 Because -2 + 2 is equal to zero both 'twos' disappear. The x is alone.

  15. Breaking it down … Let’s say we were given this statement 3x How can we get rid of the 3 so we keep only the x? Well, if the number 3 is multiplying by x … we simply divide by 3 to get 3x x Because 3 divided by 3 is equal to 1 we get x alone. 3

  16. Let’s say we were given this statement x 5 How can we get rid of the 5 so we keep only the x? The x is being divided by 5. In this case we multiply also by 5. 5x As 5 divided by 5 is equal to 1 both fives disappear. The result is that we keep the x alone, as we wanted. x 5

  17. What does ‘equation’ mean? An equation looks like this: 3x – 4 = 7 + 2x And your main goal is to solve the equation so you get the value of the x (not known at this time) that makes the formula correct.

  18. 3x – 4 = 7 + 2x Solving means to know the value for 'x'. We know the value of 'x' when we can say: 'x' is equal to … the left side of the equal sign. X = ? Most important rule: Because both sides of an equation are EQUAL, any operation we do on one side must be done on the other side.

  19. x = # First step: Decide which side the variable will be on and write it above the equation. 3x – 4 = 7 + 2x This will help you remember which side you are moving the # to and which side you are moving the variable to. Most important rule: Because both sides of an equation are EQUAL, any operation we do on one side must be done on the other side.

  20. x = # 3x – 4 = 7 + 2x -2x - 2x Re-write what is left after you get your variable or # to one side. x – 4 = 7 Most important rule: Because both sides of an equation are EQUAL, any operation we do on one side must be done on the other side.

  21. x = # x – 4 = 7 +4 +4 Now that my Variable is on the correct side, I need to get all my numbers to one side so the X stands alone. Continue with opposite math. Look at your diagram to get the #s where you wanted them. (x = #) x = 11 Re-write what is left. Most important rule: Because both sides of an equation are EQUAL, any operation we do on one side must be done on the other side.

  22. Check your work 3x – 4 = 7 + 2x Replace the variable with your solution – then solve. 3 * (11) – 4 = 7 + 2 * (11) 33 – 4 = 7 + 22 29 = 29

  23. Ta-Dah! You just correctly did Algebra!!!

  24. Powerpoint Assembled by: Mrs. Sinclair Step-by-step instructions from: http://elementaryalgebra.pages3d.net/ Images from: funbrain.com digitalweddingforum.com

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