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Mastering Linear Equations: Techniques and Solutions

Learn to solve linear equations, understand properties of equality, deal with decimals, and work with formulas effectively. Perfect for mastering algebraic problem-solving skills.

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Mastering Linear Equations: Techniques and Solutions

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  1. Determine whether a number is a solution of a given equation. A OBJECTIVES

  2. Solve linear equations using the properties of equality. B OBJECTIVES

  3. Solve linear equations in one variable using the six-step procedure(CRAM). C OBJECTIVES

  4. Solve linear equations involving decimals. D OBJECTIVES

  5. Section 2.1 Linear Equations in One Variable

  6. DEFINITION PROPERTIES OF EQUALITIES For real numbers a, b, and c. a = a Reflexive If a = b, then b = a Symmetric If a = b and b = c, then a = c Transitive

  7. DEFINITION LINEAR EQUATIONS An equation that can be written in the form:

  8. DEFINITION SOLUTIONS OF AN EQUATION Replacements of the variable that make the equation a true statement.

  9. DEFINITION EQUIVALENT EQUATIONS Two equations that have the same solution set.

  10. PROCEDURE Clearfractions/decimals Removeparentheses/simplify Add/Subtract to get variable isolated Multiply/Divide to make coefficient 1

  11. DEFINITION EQUATIONS WITH NO SOLUTIONS AND INFINITELY MANY SOLUTIONS No solutions(contradictions): Infinitely many solutions(identities):

  12. Solve a formula for a specified variable and then evaluate the answer for given values of the variables. A OBJECTIVES

  13. Write a formula for a given situation that has been described in words. B OBJECTIVES

  14. Solve problems about angle measures. C OBJECTIVES

  15. Section 2.2 Formulas, Geometry and Problem Solving

  16. PROCEDURE SOLVE FOR A SPECIFIED VALUE Add or Subtract the same quantity on both sides. Use the distributive property. Use CRAM.

  17. Translate a word expression into a mathematical expression. A OBJECTIVES

  18. Solve word problems of a general nature. B OBJECTIVES

  19. Solve word problems about integers. C OBJECTIVES

  20. Solve word problems about geometric formulas and angles. D OBJECTIVES

  21. Section 2.3 Problem Solving: Integers and Geometry

  22. PROCEDURE: RSTUV Method for Solving Word Problems Read Select Think Use Verify

  23. Solve percent problems. A OBJECTIVES

  24. Solve investment problems. B OBJECTIVES

  25. Solve uniform motion problems. C OBJECTIVES

  26. Solve mixture problems. D OBJECTIVES

  27. Section 2.4 Problem Solving: Percent, Investment, Motion, and Mixture Problems

  28. PROCEDURE: RSTUV Method for Solving Word Problems Read Select Think Use Verify

  29. Graph linear inequalities. A OBJECTIVES

  30. Solve and graph linear inequalities. B OBJECTIVES

  31. Solve and graph compound inequalities. C OBJECTIVES

  32. Use the inequality symbols to translate sentences into inequalities. D OBJECTIVES

  33. Section 2.5 Linear and Compound Inequalities

  34. DEFINITION LINEAR INEQUALITIES An inequality that can be written in the form:

  35. DEFINITION UNION OF TWO SETS

  36. DEFINITION INTERSECTION OF TWO SETS

  37. DEFINITION EQUIVALENT STATEMENTS FOR “AND”

  38. Solve absolute-value equations. A OBJECTIVES

  39. Solve absolute-value inequalities of the form |ax + b| < c or |ax + b| > c, where c > 0. B OBJECTIVES

  40. Section 2.6 Absolute-Value Equations and Inequality

  41. DEFINITION THE SOLUTIONS OF |X| = A (A ≥ 0) If a ≥ 0, the solutions of |x| = a are x = a and x = –a.

  42. STATEMENT TRANSLATION ABSOLUTE VALUE EQUATIONS If |expression| = a, where a ≥ 0 expression = a or –a

  43. STATEMENT TRANSLATION ABSOLUTE VALUE EQUATIONS If |expression| = |expression|, expression = expression expression = – (expression)

  44. STATEMENT TRANSLATION |x| = 2: x is exactly 2 units from 0 |x| < 2: x is less than 2 units from 0 |x| > 2: x is more than 2 units from 0 0 0 0

  45. DEFINITION |x| < a is equivalent to –a < x < a

  46. DEFINITION |x| > a is equivalent to x < –a or x > a

  47. Chapter 2 Linear Equationsand Inequalities Section 2.1

  48. Chapter 2 Linear Equationsand Inequalities Section 2.1Exercise #5

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