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INTEGRATING EQUATIONS

INTEGRATING EQUATIONS. PUTTING IT ALL TOGETHER. Get rid of ( ). DISTRIBUTE Get rid of fractions. Multiply by LCD Combine any like terms on the SAME side of the equal sign. Add or Subtract. Move ALL variables to one side. Move all constants to the opposite side.

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INTEGRATING EQUATIONS

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  1. INTEGRATINGEQUATIONS PUTTING IT ALL TOGETHER

  2. Get rid of ( ). DISTRIBUTE Get rid of fractions. Multiply by LCD Combine any like terms on the SAME side of the equal sign. Add or Subtract Move ALL variables to one side. Move all constants to the opposite side. Either add or subtract to do this step. (remember, use the opposite) 3 STAGES OF SOLVING EQUATIONS Isolate Solve Simplify • The only thing left to do now is either MULTIPLY or DIVIDE by the coefficient in front of the variable. (remember, use the opposite)

  3. The easy ones, from the END? “fix” double signs first 1. X + 2.2 = 9.2 2. Y + (-6) = 3 - 2.2 - 2.2 Y - 6 = 3 + 6 +6 X = 7 Y = 9 (3) (3) 4. 3. 9x = 45 9 9 36 2n = x = 5 2 2 n = 18

  4. Now, the MIDDLE and the END First step, ISOLATE – “undo” the addition or subtraction 5. Second step – SOLVE – “undo” the multiplication or division First step, ISOLATE – “undo” the addition or subtraction 6. Second step – SOLVE – “undo” the multiplication or division

  5. Now from the beginning....Simplify! Let’s Review Simplifying equations involves three steps. • Getting rid of parentheses. • To remove parentheses from an equation, distribute. • Getting rid of fractions. • To remove a fraction from an equation multiply each term by the LCD. • Getting rid of like terms that are on the SAME side of the equal sign. • Combine like terms by adding or subtracting using your integer rules.

  6. Ex. 7 • Any Parentheses? • YES - Then Distribute • Any Fractions? • NO • Any Like Terms? • NO • Then ISOLATE • Now SOLVE

  7. ? Simplify - Distribute 1 Simplify - Like Terms Isolate Solve

  8. Ex. 9 • Any Parentheses? • NO • Any Fractions? • YES – multiply by the LCD. • Any Like Terms? • NO • Then ISOLATE • Now SOLVE

  9. Ex. 10 • No ( ) so…. • Multiply by the LCD • Group like terms • Combine like terms • Use integer rules • Now Isolate. • and Solve

  10. Ex. 11 • Any Parentheses? • NO • Any Fractions? • NO • Any Like Terms? • YES – combine like terms using integer rules. • Then ISOLATE • Now SOLVE

  11. Now let’s put it all together… Ex. 12 • Parentheses – YES Distribute and Separate. • Get rid of the LCD. What is it? • Isolate – variables left, constants right. • Solve - divide

  12. Ex. 13 • Distribute and Separate. • Get rid of the LCD. What is it? • Isolate – variables left, constants right. • Solve - divide

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