	Algebra Tutorials!

Thursday 21st of November



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	Rotating a Parabola
	Multiplying Fractions
	Finding Factors
	Miscellaneous Equations
	Mixed Numbers and Improper Fractions
	Systems of Equations in Two Variables
	Literal Numbers
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	Subtracting Integers
	Simplifying Complex Fractions
	Decimals and Fractions
	Multiplying Integers
	Logarithmic Functions
	Multiplying Monomials
	Mixed
	The Square of a Binomial
	Factoring Trinomials
	The Pythagorean Theorem
	Solving Radical Equations in One Variable
	Multiplying Binomials Using the FOIL Method
	Imaginary Numbers
	Solving Quadratic Equations Using the Quadratic Formula
	Solving Quadratic Equations
	Algebra
	Order of Operations
	Dividing Complex Numbers
	Polynomials
	The Appearance of a Polynomial Equation
	Standard Form of a Line
	Positive Integral Divisors
	Dividing Fractions
	Solving Linear Systems of Equations by Elimination
	Factoring
	Multiplying and Dividing Square Roots
	Functions and Graphs
	Dividing Polynomials
	Solving Rational Equations
	Numbers
	Use of Parentheses or Brackets (The Distributive Law)
	Multiplying and Dividing by Monomials
	Solving Quadratic Equations by Graphing
	Multiplying Decimals
	Use of Parentheses or Brackets (The Distributive Law)
	Simplifying Complex Fractions 1
	Adding Fractions
	Simplifying Complex Fractions
	Solutions to Linear Equations in Two Variables
	Quadratic Expressions Completing Squares
	Dividing Radical Expressions
	Rise and Run
	Graphing Exponential Functions
	Multiplying by a Monomial
	The Cartesian Coordinate System
	Writing the Terms of a Polynomial in Descending Order
	Fractions
	Polynomials
	Quadratic Expressions
	Solving Inequalities
	Solving Rational Inequalities with a Sign Graph
	Solving Linear Equations
	Solving an Equation with Two Radical Terms
	Simplifying Rational Expressions
	Exponents
	Intercepts of a Line
	Completing the Square
	Order of Operations
	Factoring Trinomials
	Solving Linear Equations
	Solving Multi-Step Inequalities
	Solving Quadratic Equations Graphically and Algebraically
	Collecting Like Terms
	Solving Equations with Radicals and Exponents
	Percent of Change
	Powers of ten (Scientific Notation)
	Comparing Integers on a Number Line
	Solving Systems of Equations Using Substitution
	Factoring Out the Greatest Common Factor
	Families of Functions
	Monomial Factors
	Multiplying and Dividing Complex Numbers
	Properties of Exponents
	Multiplying Square Roots
	Radicals
	Adding or Subtracting Rational Expressions with Different Denominators
	Expressions with Variables as Exponents
	The Quadratic Formula
	Writing a Quadratic with Given Solutions
	Simplifying Square Roots
	Adding and Subtracting Square Roots
	Adding and Subtracting Rational Expressions
	Combining Like Radical Terms
	Solving Systems of Equations Using Substitution
	Dividing Polynomials
	Graphing Functions
	Product of a Sum and a Difference
	Solving First Degree Inequalities
	Solving Equations with Radicals and Exponents
	Roots and Powers
	Multiplying Numbers

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Solving Multi-Step Inequalities

Objective Learn to solve linear inequalities involving more than one operation.

This lesson is an extension of the methods you should already know to solve linear equations. The methods used are the Addition and Multiplication Properties of Inequalities, which parallel the corresponding properties for equalities. There are two significant distinctions that must be remembered.

The first is that when multiplying or dividing an inequality by a negative number, the direction of the inequality symbol must be changed.

The other is that the term “solve” is used a bit differently when speaking of inequalities. In equations, “solve” means to find a particular number that is the only solution to the equation. However, the result of solving an inequality is never a single number but rather the description of a set, such as x 5 or 22 x 7.

This distinction is very important.

Solving Inequalities

Let's begin by reviewing the properties of inequalities.

Addition and Subtraction Properties of Inequalities

Adding or subtracting a fixed number to each side of an inequality produces an equivalent inequality. Any solution of either inequality is a solution of the other.

x - 2	1
x - 2 + 2	1 + 2	Add 2 to each side.
x	23

Adding 2 to each side of the original inequality shows that x - 2 1 is equivalent to x 3.

Multiplication and Division Properties of Inequalities

• Multiplying or dividing each side of an inequality by the same positive number produces an equivalent inequality.

• Multiplying or dividing by the same negative number produces an equivalent inequality if the direction of the inequality symbol is reversed.

3x 12		-x 5
x 4	Divide each side by 3.	x -5	Multiply each side by -1.
So, 3x 12	is equivalent to x 4.	So, -x 5	is equivalent to x -5.