Algebra Tutorials!



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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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