Equations

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1Terminology

Steps for Solving

Examples

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Terms

Terminology Definition Example

Equation in x A statement of equality involving one variable, x

Solution or Root of an equation in x

A number b that yields a true statement when substituted for x

5 is a solution for x2-5=4x52-5=4(5)25-5=2020=20

A number b satisfies an equation in x

b is the solution of the equation

5 is a solution for x2-5=4x

Equivalent equations

Equations that have exactly the same solutions (solving for x)

2x+1=6x+3, -1/2 satisfies both sides

xxx 452

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Terms (cont.)

Terminology Definition Example

Solve an equation in x

Find all solutions of the equation

To solve (x+3)(X-5)=0, set each factor equal to zero:x+3=0, x-5=0, obtaining the solutions -3 and 5

Linear Equation in x

An equation that can be written in the form ax + b = 0

4x + 5 = 0

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Steps for Solving

1. Determine the lcd of the rational expressions

2. Find the values of the variable that make the lcd equal to zero. These are NOT solutions!

3. Multiply Each Term of the equation by the lcd

4. Simplify! Simplify! Simplify! 5. Factor if necessary 6. Solve for the given variable

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Examples

Solve the equation 6x – 7 + 2x + 5

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More Examples

Solve the equation (8x – 2)(3x-4) = (4x+3)(6x – 1)

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Even More Examples

Solve the equation

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Even More Examples (cont.)

CHECK YOUR WORK!

Not all problems have a solution You can follow all of the steps perfectly

and still have no valid solution

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Practice Problems

Page 66Problems 1-30