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Rational Expressions
Graphs of Rational Functions
Solve Two-Step Equations
Multiply, Dividing; Exponents; Square Roots; and Solving Equations
LinearEquations
Solving a Quadratic Equation
Systems of Linear Equations Introduction
Equations and Inequalities
Solving 2nd Degree Equations
Review Solving Quadratic Equations
System of Equations
Solving Equations & Inequalities
Linear Equations Functions Zeros, and Applications
Rational Expressions and Functions
Linear equations in two variables
Lesson Plan for Comparing and Ordering Rational Numbers
LinearEquations
Solving Equations
Radicals and Rational Exponents
Solving Linear Equations
Systems of Linear Equations
Solving Exponential and Logarithmic Equations
Solving Systems of Linear Equations
DISTANCE,CIRCLES,AND QUADRATIC EQUATIONS
Solving Quadratic Equations
Quadratic and Rational Inequalit
Applications of Systems of Linear Equations in Two Variables
Systems of Linear Equations
Test Description for RATIONAL EX
Exponential and Logarithmic Equations
Systems of Linear Equations: Cramer's Rule
Introduction to Systems of Linear Equations
Literal Equations & Formula
Equations and Inequalities with Absolute Value
Rational Expressions
SOLVING LINEAR AND QUADRATIC EQUATIONS
Steepest Descent for Solving Linear Equations
The Quadratic Equation
Linear equations in two variables
   
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Solving Linear Equations

Consider the equation:

3x − 5 =13

We are undoing what is happening to x ( Multiplication by 3 and subtraction
by 5 ) . So we undo by going backwards: undo subtraction of 5 and then
undo multiplication by 3.



Any equation that can be written in the form ax + b = c is called a linear
equation. In this section all of the equations are linear. To solve linear
equations:

1.) Simplify both sides of the equation.
2.) Collect all the variable terms and all constant terms on the

other side.

3.) Isolate the variable and solve.
4.) Then check the answer.

EXAMPLE: Solve and Check

To Solve we can do two things:
multiply by 3 or multiply by
2x = ____ divide by 2 x = ____
x = ___

EXAMPLE: Solve and Check



Sometimes it may be necessary to simplify before trying to solve. We get all
the x 's together and the constants together before we solve.

EXAMPLE: Solve and Check

Many people would love to do away with having to deal with fractions. When
an equation has fractions involved, we may use the multiplication property of
equality to clear the fractions. We multiply both sides by the LCD.

Therefore we don’t need to
deal with fractions very much.

EXAMPLE: Solve:

IDENTITIES AND IMPOSSIBLE EQUATIONS:

The equations that we have been solving are called conditional equations
because they only work for one number. An equation that is true for all values
of its variable is called an identity.

3( x + 2) = 3x + 6 is an identity

2x + 2 = 2x + 3 is an equation that is never true.

Solve the above equation to see what happens:

EXAMPLE: Solve the equation.

a.) −3( s + 2) = −2( s + 4) − s
EXAMPLE: A driver left the plant
with 300 bottles of drinking water on
his truck. His route consisted of
office buildings, each of which
received 3 bottles of water. The
driver returned to the plant with 117
bottles on the truck. To how many
office buildings did he deliver?
EXAMPLE: The formula:
models the recommended weight, W ,
in pounds, for a male, where H
represents the man’s height , in inches,
over 5 feet. What is the recommended
weight for a man who is 6 feet, 3
inches tall?
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