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__

- 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

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