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# Solving-Equations-Algebraically

last edited by 11 years, 11 months ago

solvingequations.pbwiki.com

# Solving Equations Algebraically

Porpose-

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

# Solving Equations Involving Fractions

ex. (x/2)+(6x/7)=(19/14)

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

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)

# 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