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Solving Equations Using Addition and Subtraction

Solving Equations Using Addition and Subtraction. Objectives :. A.4f Apply these skills to solve practical problems. A.4b Justify steps used in solving equations. Use a graphing calculator to check your solutions. To Solve an Equation means.

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Solving Equations Using Addition and Subtraction

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  1. Solving Equations Using Addition and Subtraction Objectives: • A.4f Apply these skills to solve practical problems. • A.4b Justify steps used in solving equations. • Use a graphing calculator to check your solutions.

  2. To Solve an Equation means... • To isolate the variable having a coefficient of 1 on one side of the equation. • Ex: x = 5 is solved for x. • y = 2x - 1 is solved for y.

  3. Addition Property of Equality What it means: For any numbers a, b, and c, if a = b, then a + c = b + c. You can add any number to BOTH sides of an equation and the equation will still hold true.

  4. We all know that 7 = 7. Does 7 + 4 = 7? NO! But 7 + 4 = 7 + 4. The equation is still true if we add 4 to both sides. An easy example: • Would you ever leave the house with only one shoe on? • Would you ever put blush on just one cheek? • Would you ever shave just one side of your face?

  5. x - 6 = 10 Add 6 to each side. x - 6 = 10 +6 +6 x = 16 Always check your solution!! The original problem is x - 6 = 10. Using the solution x=16, Does 16 - 6 = 10? YES! 10 = 10 and our solution is correct. Let’s try another example!

  6. Recall that y + (-4) = 9 is the same as y - 4 = 9. Now we can use the addition property. y - 4 = 9 +4 +4 y = 13 Check your solution! Does 13 - 4 = 9? YES! 9=9 and our solution is correct. What if we see y + (-4) = 9?

  7. Remember to always use the sign in front of the number. Because 16 is negative, we need to add 16 to both sides. -16 + z = 7 +16 +16 z = 23 Check you solution! Does -16 + 23 = 7? YES! 7 = 7 and our solution is correct. How about -16 + z = 7?

  8. -n - 10 = 5 +10 +10 -n = 15 Do we want -n? NO, we want positive n. If the opposite of n is positive 15, then n must be negative 15. Solution: n = -15 Check your solution! Does -(-15)-10=5? Remember, two negatives = a positive 15 - 10 = 5 so our solution is correct. A trick question...

  9. Subtraction Property of Equality • For any numbers a, b, and c, if a = b, then a - c = b - c. What it means: • You can subtract any number from BOTH sides of an equation and the equation will still hold true.

  10. 1) x + 3 = 17 -3 -3 x = 14 Does 14 + 3 = 17? 2) 13 + y = 20 -13 -13 y = 7 Does 13 + 7 = 20? 3) z - (-5) = -13 Change this equation. z + 5 = -13 -5 -5 z = -18 Does -18 -(-5) = -13? -18 + 5 = -13 -13 = -13 YES! 3 Examples:

  11. Try these on your own...

  12. The answers...

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