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Math 71 Intermediate Algebra

 
  • Sample of what you should know before taking Math 71:
    1. Solve open parenthesis 2 x minus 5 close parenthesis times open parenthesis x plus 1 close parenthesis equals 72
     2. Solve start square root 3 x plus 7 end square root equals 3 x plus 5
      • Solution
        3 x plus 7 equals 9 x squared plus 30 x plus 25
        9 x squared plus 27 x plus 18 equals 0
        9 times open parenthesis x plus 2 close parenthesis times open parenthesis x plus 1 close parenthesis equals 0
        x equals negative 1x equals negative 2; but x equals negative 2 does not work, thus x equals negative 1
     3. Graph the solutions set y greater than negative 2 thirds x plus 5
     4. Simplify start fraction 5 over x squared minus 2 x end fraction plus start fraction 8 over x end fraction minus start fraction 10 x over x minus 2 end fraction
     5. How many mL of a 15% acid solution and how many mL of a 3% acid solution must be mixed to get 45 mL of a 7% acid solution?
      • Solution
        Let x = amount of 15% acid solution and y = amount of 3% acid solution.
        0 point 1 5 x plus 0 point 0 3 times open parenthesis 45 minus x close parenthesis equals 0 point 0 7 times open parenthesis 45 close parenthesis
        0 point 1 2 x plus 1 point 3 5 equals 3 point 1 5
        0 point 1 2 x equals 1 point 8
        x equals 15
        15 mL of 15% acid solution and 30 mL of 3% acid solution

     

  • Sample of what you will learn in Math 71:
    1. Graph f of x equals 2 x squared minus 8 x minus 3
     2. Solve and write your answer in exact form  2 e superscript x minus 4 baseline plus 7 equals 19
     3. Solve and write your answer using interval notation  start absolute value 2 x minus 1 end absolute value greater than 3
      • Solution
        2 x minus 1 greater than 3  or  2 x minus 1 less than negative 3
        2 x greater than 4  or  2 x less than negative 2
        x greater than 2  or  x less than negative 1

        open parenthesis negative infinity comma negative 1 close parenthesis union open parenthesis 2 comma infinity close parenthesis

     4. Solve  open parenthesis x squared minus 2 close parenthesis squared minus open parenthesis x squared minus 2 close parenthesis minus 6 equals 0