solvingequations.pbwiki.com

Solving Equations Algebraically

Porpose-

to informe the masses about how to use algebra to solve equations.

outline:

-Solving equations involving fractions

-Equations with and extraneous solutions 

-When to check for extraneous

-Approximating solutions of an equation graphically

-Finding points of intersection graphically

-Solving polynomial equations algebraically

Solving Equations Involving Fractions

ex. (x/2)+(6x/7)=(19/14)          

     (7x/14)+(12x/14)=(19/14)     -find common denominators for the fractions.

     (19x/14)=(19/14)                         -add the two

  x=1                                             -solve

ex.(5/2x)-(4/ x)=3               

Equations with an Extraneous Solutions

ex. (1/x-2)=(3/x+2)-(6x/x^2-4)     -Find the least common denominator..(x+2)(x-2)

     x+2=3(x-2)-6x                    -simplify the equations

      x+2=3x-6-6x                     -distribute the 3

     4x=-8                               -get x's on the same side alone

     x=-2                                  -solve

If you plug in -2 to check you find that is turns up with a denominator of zero. so x=-2 is extraneous

When to check solutions

1. fractions with an x in the denominator
2. equations with square roots
3. equations with absolute values 

Approximating Solutions of an Equation Graphically

ex. y=12-4x     -type into your calculator and graph

-then zoom in on the point until you can approximate the x-intercept (3)

ex. y=(x^2)-2.5x-6     -plug the equation into your calculator set to y and graph                             

                              -zoom into the x-intercepts, they are the answers (-1.5,4)

www.sitmo.com/latex/

Finding Points of Intersection

ex. y=9-2x              

       y=x-3     

       9-2x=x-3       -set equations equal to each other and solve for x

        x=1 

ex. y=2x^2          - set both equations equal to y

       y=x^4-2x^2  - graph them. the point of intersection is the solution.

Solving Polynomial Equations Algebraically

ex.x^2+10x+25     -first check to see if you can take out a greatest common factor

     (x+5)(x+5)          -factor the equation

     x=-5                    -use the opposite of 5 as the answer

ex.x^2+5x-6          -check for GCF

     (x+6)(x-1)          -factor

          x=-6,1            -opp. of 6 and -1

NOTE: IF YOU CANNOT FACTOR YOU MUST USE.....QUADRATIC FORMULA