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Solving Equations Using Addition and Subtraction (3.1)

Solving Equations Using Addition and Subtraction (3.1). 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. Objectives :. To Solve an Equation means.

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Solving Equations Using Addition and Subtraction (3.1)

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  1. Solving Equations Using Addition and Subtraction (3.1) • 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. Objectives:

  2. To Solve an Equation means... • To isolate the variable 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 For any numbers a, b, and c, if a = b, then a+ c= b+ c. What it means: You can add any number to BOTH sides of an equation and the equation will still hold true.

  4. An easy example: • Think about it… • 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? • Would you ever add a number to just one side of an equation? • I hope you answered “No!” to all of these. 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.

  5. Let’s try another example! 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.

  6. What if we see y + (-4) = 9? 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.

  7. How about -16 + z = 7? • Remember to always use the sign in front of the number. • 16 is negative, so 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.

  8. A trick question... -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.

  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. 3 Examples: 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!

  11. Answer Now Solve x + 2 = -3To get the variable by itself, what is your first step? • Add 2 to both sides • Subtract 2 from both sides • Add 3 to both sides • Subtract 3 from both sides

  12. Answer Now Solve 8 = m - 3 • m = 5 • m = 11 • m = 24 • m = 8/3

  13. Answer Now Solve -y – (-3) = 7 • y = 10 • y = 4 • y = -10 • y = -4

  14. Try these on your own...

  15. The answers...

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