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Algebra II Equations and Properties for Solving Equations

Learn about equations, inverse operations, commutative property, identity property of addition, and subtractions rules of zero in Algebra II. Practice solving equations with examples and variables.

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Algebra II Equations and Properties for Solving Equations

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  1. Algebra II By Monica Yuskaitis Free powerpoints at http://www.worldofteaching.com

  2. Definitions • Equation – A mathematical sentence stating that 2 expressions are equal. • 12 – 3 = 9 • 8 + 4 = 12

  3. Definitions • Equation – A mathematical sentence with an equals sign. • 16 – 5 = 11 • 14 + 3 = 17

  4. Definitions • Equals Sign (=) Means that the amount is the same on both sides. • 4 + 2 = 6 • 5 – 2 = 3

  5. An Equation is like a balance scale. Everything must be equal on both sides. = 10 5 + 5

  6. When the amounts are equal on both sides it is a true equation. = 12 6 + 6

  7. When the amounts are unequal on both sides it is a false equation. = 8 2 + 2

  8. When an amount is unknown on one side of the equation it is an open equation. = 7 n + 2

  9. When you find a number for n you change the open equation to a true equation. You solve the equation. = 7 5 n + 2

  10. Are these equations true, false or open? false • 11 - 3 = 5 • 13 + 4 = 17 • N + 4 = 7 • 12 – 3 = 8 • 3 + v = 13 • 15 – 6 = 9 true open false open true

  11. Definitions • Inverse operation – the opposite operation used to undo the first. • 4 + 3 = 7 7 – 4 = 3 • 6 x 6 = 36 36 / 6 = 6

  12. How to solve an addition equation • Use the inverse operation for addition which is subtraction • m+ 8 = 12 12 - 8 = 4 • m = 4 4 + 8 = 12

  13. How to solve a subtraction equation • Use the inverse operation for subtraction which is addition • m- 3 = 5 5 + 3 = 8 • m = 8 8 - 3 = 5

  14. Solve these equations using the inverse operations 3 • n + 4 = 7 • n – 5 = 4 • n + 4 = 17 • n – 6 = 13 • n + 7 = 15 • n – 8 = 17 9 13 19 8 9

  15. Commutative Property • 5 + 4 = 9 4 + 5 = 9 • a + b = c b + a = c • 6 + 3 = 9 3 + 6 = 9 • x+ y = z y + x = z • 3 + 4 + 1 = 8 1 + 3 + 4 = 8

  16. Solve these equations using the commutative property n = 4 • n + 7 = 7 + 4 • m + 2 = 2 + 5 • z + 3 = 3 + 9 • g + 6 = 6 + 11 • s + 4 = 4 + 20 • c + 8 = 8 + 32 m = 5 z = 9 g = 11 s = 20 c = 32

  17. The Identity Property of Addition • 7 + 0 = 7 • a + 0 = a • 8 + 0 = 8 • c + 0 = c • 2 + 0 = 2

  18. Use the Identity Property of addition to solve these problems • n + 0 = 8 • b + 0 = 7 • m + 0 = 3 • v + 0 = 5 • w + 0 = 4 • r + 0 = 2 n = 8 b = 7 m = 3 v = 5 w = 4 r = 2

  19. Subtraction Rules of zero • 7 – 7 = 0 • n – n = 0 • 4 – 0 = 4 • n – 0 = n

  20. Find the value of n using the rules of subtraction • n - 8 = 0 • n – 9 = 0 • n – 0 = 7 • n – 0 = 9 • n – 7 = 0 • n – 0 = 5 n = 8 n = 9 n = 7 n = 9 n = 7 n = 5

  21. Write an equation for these problems using a variable • Timothy got 72 right on his timed test in July. He got 99 right on this same test in November. • Jasmin runs 15 minutes before school and 30 minutes after school. • One zinger costs 25 cents. Issak bought 4. 72 + n = 99 or 99 – 72 = n 15 + 30 = n 4 x 25 = n

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