Math 71 Intermediate Algebra

If you are considering taking a lower-level class than Math 71:
- We encourage you to consider taking the corequisite course—Math 7—which provides additional support for Math 71.
- You might consider taking the two-semester Math 71A/71B sequence, which covers the same material as Math 71, but at a slower pace.
- The next level lower is Math 51 (Elementary Algebra).
If you are considering taking a higher-level class than Math 71:

Your options are:

Sample of what you should know before taking Math 71:

1. Solve $open parenthesis 2 x minus 5 close parenthesis times open parenthesis x plus 1 close parenthesis equals 72$
- - Solution
    
    $2 x squared minus 3 x minus 5 equals 72$
    
    $2 x squared minus 3 x minus 77 equals 0$
    
    $open parenthesis 2 x plus 11 close parenthesis times open parenthesis x minus 7 close parenthesis equals 0$
    
    $x equals negative 11 over 2$ , $x equals 7$
2. Solve $start square root 3 x plus 7 end square root equals 3 x plus 5$
- - Solution
    
    $3 x plus 7 equals 9 x squared plus 30 x plus 25$
    
    $9 x squared plus 27 x plus 18 equals 0$
    
    $9 times open parenthesis x plus 2 close parenthesis times open parenthesis x plus 1 close parenthesis equals 0$
    
    $x equals negative 1$ , $x equals negative 2$ ; but $x equals negative 2$ does not work, thus $x equals negative 1$
3. Graph the solutions set $y greater than negative 2 thirds x plus 5$
- - Solution
    $graph of a dotted line going down from left to right with slope negative 2 over 3 and passing through the y axis at the point 0 5 with the region above the line shaded$
4. Simplify $start fraction 5 over x squared minus 2 x end fraction plus start fraction 8 over x end fraction minus start fraction 10 x over x minus 2 end fraction$
- - Solution
    
    $start fraction 5 plus 8 times open parenthesis x minus 2 close parenthesis minus 10 x times open parenthesis x close parenthesis over x times open parenthesis x minus 2 close parenthesis end fraction$
    
    $start fraction negative 10 x squared plus 8 x minus 11 over x times open parenthesis x minus 2 close parenthesis end fraction$
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 $f of x equals 2 x squared minus 8 x minus 3$
- - Solution
    $graph of upward facing parabola with vertex 2 comma negative 11 and passing through the point 0 comma negative 3$
2. Solve and write your answer in exact form $2 e superscript x minus 4 baseline plus 7 equals 19$
- - Solution
    
    $2 e superscript x minus 4 baseline plus 7 equals 19$
    
    $2 e superscript x minus 4 baseline equals 12$
    
    $e superscript x minus 4 baseline equals 6$
    
    $x minus 4 equals l n 6$
    
    $x equals 4 plus l n 6$
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 $open parenthesis x squared minus 2 close parenthesis squared minus open parenthesis x squared minus 2 close parenthesis minus 6 equals 0$
- - Solution
    
    Let $u equals open parenthesis x squared minus 2 close parenthesis$
    
    equation becomes $u squared minus u minus 6 equals 0$
    
    $open parenthesis u minus 3 close parenthesis times open parenthesis u plus 2 close parenthesis equals 0$
    
    $open parenthesis x squared minus 2 minus 3 close parenthesis times open parenthesis x squared minus 2 plus 2 close parenthesis equals 0$
    
    $open parenthesis x squared minus 5 close parenthesis times x squared equals 0$
    
    $x equals plus or minus square root of 5$ , $x equals 0$

Math 71 Intermediate Algebra

If you are considering taking a lower-level class than Math 71:

If you are considering taking a higher-level class than Math 71:

Sample of what you should know before taking Math 71:

Sample of what you will learn in Math 71: