Algebra Tutorials!  
Wednesday 17th of April
Rotating a Parabola
Multiplying Fractions
Finding Factors
Miscellaneous Equations
Mixed Numbers and Improper Fractions
Systems of Equations in Two Variables
Literal Numbers
Adding and Subtracting Polynomials
Subtracting Integers
Simplifying Complex Fractions
Decimals and Fractions
Multiplying Integers
Logarithmic Functions
Multiplying Monomials
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
Order of Operations
Dividing Complex Numbers
The Appearance of a Polynomial Equation
Standard Form of a Line
Positive Integral Divisors
Dividing Fractions
Solving Linear Systems of Equations by Elimination
Multiplying and Dividing Square Roots
Functions and Graphs
Dividing Polynomials
Solving Rational Equations
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
Quadratic Expressions
Solving Inequalities
Solving Rational Inequalities with a Sign Graph
Solving Linear Equations
Solving an Equation with Two Radical Terms
Simplifying Rational Expressions
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
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.



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