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S tandard #1: Write an Algebraic E xpression from a word problem.

Learn how to convert word problems into algebraic expressions, combine like terms, evaluate expressions, solve one-step, two-step, and multi-step equations, write and solve equations from word problems, and solve absolute value equations and inequalities.

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S tandard #1: Write an Algebraic E xpression from a word problem.

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  1. Standard #1:Write an Algebraic Expression from a word problem. Text Section: 1.1

  2. Reminders KEY WORDS • Sum, Increased by, More Than, Plus • Difference, Less Than, Decreased by • Product, Per, Groups of, Times • Quotient, Divided by, Ratio

  3. Examples

  4. Answers

  5. Standard #2:Combine like terms in an expression. Text Section: 1.7

  6. Reminders • Distribute First (if necessary) • Combine ONLY if they have the SAME variable AND SAME exponent!

  7. Examples 1. 12x + 30x 2. 6.8y2– y2 3. 4n + 11n2 4. 1/2x3+ 3/4x3 5. 2(x + 6) + 3x 6. 9 + (x – 4)6   7. -3(-2 – x) + 8

  8. Answers 1. 42x 2. 5.8y2 • 4n + 11n2 4. 1 1/4x3 5. 5x + 12 6. 6x - 15 7. 3x + 14

  9. Standard #3:Evaluate an expression. Text Section: 1.6

  10. Reminders • Use Parentheses when you substitute in for a Variable. • PEMDAS!!!

  11. Examples • 5(1-2) – (3-2) • – 9 – (-18) + 6 • 16 [5- (3 + 2²)] • 7x (3 + 2x) for x = -1

  12. Answers • -6 • 15 • -32 • -7

  13. Standard #4:Solve a 1 step equation. Text Section: 2.1-2.2

  14. Reminders 5 Steps! X + 3 = 10 - 3 - 3 X = 10 -3 X= 7 7 + 3 = 10

  15. Examples 1. n – 3.2 = 5.6 2. x + 7 = 9 3. m= 1.5 3 4. 16 = 4c

  16. Answers 1. n = 8.8 2. x = 2 3. m = 4.5 4. 4 = c

  17. Standard #5:Solve a 2 step equation. Text Section: 2.3

  18. Reminders D C (no M) S then 8 STEPS! 2x – 3 = 13 + 3 + 3 2x = 13 + 3 2x = 16 2 2 x = 16/2 x = 8 2(8)- 3 = 13

  19. Examples • 6x + 3 – 8x = 13 • 9 = 6 – (x + 2) 3. 2a + 3 – 8a = 8 4. 4(x – 2) + 2x = 40

  20. Answers • x= -5 • x = -5 3. a= -5/6 4. x= 8

  21. Standard #6:Solve a Multi-step equation. Text Section: 2.4

  22. Reminders DCMS (YES, in that order!)

  23. Examples 1. 7k = 4k + 15 2. 4b + 2 = 3b 3. 2(y + 6) = 3y 4. 3 – 5b + 2b = -2 – 2(1 – b)

  24. Answers 1. K = 5 2. B = -2 3. Y = 12 4. B = 7/5

  25. Standard #7:Write and solve an equation from a word problem. Text Section: 2.1-2.4

  26. Reminders • Use Key words, write the equation and solve. • You may need to use DCMS, 5 steps or 8 steps

  27. Examples A person’s maximum heart rate is the highest rate, in beats per minute that the person’s heart should reach. One method to estimate maximum heart rate states that your age added to your maximum heart rate is 220. Using this method, write and solve an equation to find the maximum heart rate of a 15-year-old.

  28. Answers 15 + x = 220 X = 205

  29. Standard #8:Solve an Absolute Value Equation. Text Section: Ch 2 Extension

  30. Reminders IS IT ALONE???? IS IT NEGATIVE? • If an absolute value equation equals a positive number there are two solutions. • If an absolute value equation equals 0 there is one solution. • If an absolute vale equation equals a negative number there are no solutions.

  31. Examples • 4|x + 2| = 20 • |x| - 3 = 4 • |x + 3| + 4 = 4 • 5 = |x + 2| + 8

  32. Answers • x = 3, x = -7 2. x = 7, x = -7 • x = -3 • no solution

  33. Standard #9:Isolate a Variable. Text Section: 2.5

  34. Reminders • Use Opposite Operations to get the Letter all by itself.

  35. Examples • Given d = rt, solve for t 2. Given A = ½ bh, solve for b • Solve m – n = 5 for m • Solve m = x for k k

  36. Answers • t = d/r 2. B = 2a/h • M = 5 + n • K = m x

  37. Standard #10:Write an inequality from a word problem. Text Section: 3.1

  38. Reminders

  39. Examples Write in Words • b < - 1.5 • r ≥ 2 • 5 ≥ w 4. -1/2 < a

  40. Answers • All real numbers less than - 1.5 • All real numbers greater than or equal to 2 • All real numbers less than or equal to 5 4. All real numbers less than - 1/2

  41. Standard #11:Solve an inequality by adding and subtracting. Text Section: 3.2-3.3

  42. Reminders Same 5 Steps as solving an Equation. X + 3 < 10 - 3 -3 X < 10 -3 X< 7

  43. Examples • x + 9 < 15 • d – 3 > - 6 • 0.7 ≥ n – 0.4 4. 2 ½ ≥ - 3 + t

  44. Answers • x < 6 • d > - 3 • n< 1.1 4. T < 5 ½

  45. Standard #12:Solve an inequality by multiplying and dividing. Text Section: 3.4-3.5

  46. Reminders SAME 5 or 8 Steps with 1 TRICK If you Multiply or Divide BY (not into) a Negative- you MUST flip the inequality SIGN!

  47. Examples • -50 ≥ 5q • -42 ≤ 7x 3. 10 ≥ -x

  48. Answers • q≥ -10 • x ≥ -6 3. x ≥ -10

  49. Standard #13:Solve an Absolute Value Inequality. Text Section: Ch 3 Extension

  50. Reminders IS IT ALONE???? Set up TWO inequalities: Flip the sign AND Negative! **Tip: Remember “less thAND”** **Tip: Remember “greatOR”**

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