Solving Linear,Quadratic, Radical and Rational Equations A review unit Lesson Created by: Carol Kell

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Solving Linear,Quadratic, Radical and Rational
Equations(A review unit!)Lesson Created by
Carol Keller

• MA.AR.1.D.11
• MA.NO.3.E .11

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Concept Map
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Linear Equations

• Linear Equations are 1st Degree Polynomials
• Solve linear equations by isolating the variable
• When needed, play the I Hate Fractions Game to
  simplify the equation

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Examples of Linears

• 0 4x 12
• 2x 47 3(x 5)
• (2x 5) (x 7) ( x 6) ( 2x 3)
• 5 - (3x 7) 13

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I Hate Fractions GameThis can only be played
using equations!!!

• Find a common denominator.
• Multiply the ENTIRE equation by it.

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Common denominator is 21. Multiply everything by
21.
Math is NOT like pulling teeth!!!!
7(1 x) 3(x 2) 21(5)
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7(1 x) 3(x 2) 21(5)7 7x 3x 6
10510 x 13 10510x 92
TA-DA
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Another example
4 12 8y
16 8y.y 2
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Pros and Cons of the I Hate Fractions Game

• Can only be used with equations NOT expressions
• Works the best with LCD but will work with any
  common denominator
• Can force you to work with larger numbers but
  guarantees that you will get rid of all
  fractions!

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QuadraticsThere are 2 types of these.

• Factorable Quadratics
• Non-factorable Quadratics

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Factorable Quadratics

• Set the equation equal to 0
• Always remove Greatest Common Factors
  first.this will make the problem MUCH simpler
• Use reverse FOIL

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Factorable Quadratics
or
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Another example
or
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Yet another example!
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or
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Nonfactorable Quadratics

• Set the equation equal to 0
• Use the Quadratic Formula
• Make sure to reduce all square roots and
  fractions
• Remember that a square root of a negative number
  is complex, NOT real.

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Solving Radical Equations

• Isolate the Radical Symbol term
• Get rid of it by squaring, cubing, etcboth sides
  of the equations.
• Solve as normal..using either linear or quadratic
  rules.
• CHECK SOLUTIONSfor extraneous answers!

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Example
Isolate the radical
Square both sides
Solve as usual
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Check your solution!!!
If x 35/3 .then
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Another example
Therefore NO SOLUTION!!
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Solving Rational Equations

• Factor denominators
• Find the Least Common Multiple
• Multiply the ENTIRE equation by the LCM
• Combine like terms and solve as a linear or a
  quadratic equation.

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