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Lesson 6

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  1. Lesson 6 III. Basic Algebra

  2. A. Simplifying Algebraic Expressions Combining like terms Ex1) Ex2) 3x – 2(x + 3y) – 4y Multiplying Binomials Ex1) (x – 3)(2x + 4) Ex2)

  3. B. Solving Equations and Inequalities1. Equations Steps for Solving • Remove all fractions • Distribute • Combine like terms • Get variable on one side • Add or subtract • Multiply or divide Solve:

  4. 2. Inequalities Same steps as equations EXCEPT: when you multiply or divide both sides by a negative you must FLIP THE SIGN!!! EX) Solve and graph on a number line 6x – 3 > 8x + 7

  5. 2. Inequalities: Special Cases No Solutions Ex) 3x + 4 < 2(x + 2) + x All real number solutions Ex) 2x + 3 < 2x – 2

  6. 2. Inequalities

  7. C. Solving Rational Equations Ex) Ex)

  8. D. Evaluating and Solving Formulas Ex) Given a = -1, b = 2, c = -2, what is the value of Ex) Solve for a:

  9. E. Factoring Types of Factoring: • GCF (any number of terms) • Difference of 2 Squares & Sum of Difference of cubes (2 Terms) • Trinomial into 2 Binomials (3 terms) • Grouping (4 terms)

  10. E. Factoring: GCF Factor out the largest number and the largest variable. Once you have your answer, you should be able to distribute it and result in the original problem. Ex) Ex)

  11. E. Factoring: Difference of 2 squares or Sum /Difference of Cubes Diff of 2 Squares Pattern Ex) Sum/Diff of 2 cubes Ex) Ex)

  12. E. Factoring: Trinomial  2 Binomials • x should go first in each binomial • The numbers should multiply to give you c, and add or subtract to give you b Ex) Ex)

  13. E. Factoring: Grouping Step 1) Group the first 2 terms, factor out GCF Step 2) Group last two terms, factor out GCF Step 3) Write new binomials Ex) ax + bx + ay + by Ex) 2y + 4z + xy + 2xz

  14. E. Factoring: Extra Step Note: You may have to factor out a GCF then apply one of the factoring methods!!! Ex) Ex)

  15. E. Factoring: BOTTOM LINE Distributing leads back to original expression in standard form!!!

  16. E. Factoring

  17. F. Solving Quadratic Equations Ways of Solving • Square Root Method • Factoring • Quadratic Formula

  18. 1. Square Root Method • Algebraic, using square rooting • Don’t forget +/- Ex) Ex)

  19. 2. Factoring • Get equation = to zero • Factor • Set each factor = to zero and solve Ex) Ex)

  20. 3. Quadratic Formula • Set equation = to zero • Plug a, b, and c into the formula and solve Ex)

  21. Solve using any of the methods we have covered

  22. G. Exponents

  23. Use rules of exponents to solve

  24. H. Radicals Approximating Square Roots – being able to guess between 2 whole numbers Ex) Approximate Simplifying Ex) Ex)

  25. H. Radicals Adding and Subtracting – simplify first! Then add or subtract like radicands Ex)

  26. H. Radicals Multiplying and Dividing – Combine the numbers on the outside (mult/div), and combine the numbers on the inside (mult/div) Ex) Ex)

  27. H. Radicals Rationalizing the Denominator – The radical symbol is NOT allowed to stay in the denominator Ex) Ex.

  28. Use rules of radicals to complete the problems

  29. I. Systems of Equations Methods of Solving: • Graphing – finding where the 2 lines intersect • Substitution – plugging one equation into the other • Elimination – line up equations and eliminate a variable • Plugging in the answers

  30. I. Systems of Equations Possible Solutions: • One coordinate point: (x, y) • No solution: (lines are parallel) • Infinitely many solutions: (line are the same)

  31. Elimination Solve the following systems using the elimination method: • 3x + 2y = 10 2) 3x + 5y = 13 x – 5y = -8 2x – 2y = -2

  32. Substitution Solve the systems using the substitution method • 3x + 2y = 10 2) 2x + 4y = 6 x = 5y – 8 x + 2y = -4