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Algebra

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Examples and Solutions

Inequalities: Solve 3y + 4 > 2(y + 3) + y
 
    3y + 4 - 4 > 2y + 6 + y - 4  (Subtracting 4 from each side.)
         3y + 0 > 2y + y + 6 - 4  (Grouping like terms.)
               3y > 3y + 2          
        3y - 3y > 3y -3y + 2  (Subtracting 3y from both sides.)
                0 > 0 + 2
 Answer: 
Since y is eliminated, there are no
             values to display.

Proportions: Solve for x,  (2x + 8):(x + 2) = (2x + 5):(x + 1)
     By Proportions  (2x+8)  =  (2x+5)
                            (x+2)        (x+1)
       (2x+8)(x+1) = (2x+5)(x+2)  (Finding the Cross Products)
  2x2 + 8x + 2x + 8 = 2x2 +5x + 4x + 10  (Expanding)
        2x2 + 10x + 8 = 2x2 + 9x + 10
 2x2 - 2x2 + 10x - 9x = 10 - 8    (Rearranging)
                          
 x  = 2

 

Permutations: A permutation of a set of objects is an ordered arrangement of all the objects. How many permutations are there of a set of 4 objects, say {A, B, C, D}?

Answer: Number of permutations is 4 X 3 X 2 X 1 = 24

 

Functions: Given the function f(x) = 2x - 5x + 3. 
 Find the values of x and draw a graph of the function.

                   Let y = f(x) = 2x - 5x + 3
                      If y = f(x)
               Then y = 2x - 5x + 3
                         y = (x - 1)(2x - 3) by factorization
                When y = 0, x - 1 = 0 and 2x - 3 = 0
                    When x - 1 = 0, x = 1
                       When 2x - 3 = 0, x = 3/2 = 1
Values of x are 1 and 1

The solutions are the intercepts of the graph on the x   axis, 1 and 1.

  

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