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
- fractions with an x in the denominator
- equations with square roots
- 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)
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
Comments (1)
nneill30@... said
at 8:48 am on Dec 8, 2008
this page rocks
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