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Solving Systems of Equations Using Substitution
Simplifying Fractions 3
Factoring quadratics
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Writing Fractions as Percents
Using Patterns to Multiply Two Binomials
Adding and Subtracting Fractions
Solving Linear Inequalities
Adding Fractions
Solving Systems of Equations -
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Dividing Monomials
Multiplication can Increase or Decrease a Number
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Powers of i
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Finding the Coordinates of a Point
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Solving Equations by Factoring
Slope of a Line
Percent Introduced
Reducing Rational Expressions to Lowest Terms
The Hyperbola
Standard Form for the Equation of a Line
Multiplication by 75
Solving Quadratic Equations Using the Quadratic Formula
Raising a Product to a Power
Solving Equations with Log Terms on Each Side
Monomial Factors
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Division Property of Square and Cube Roots
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Equations of Circles
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Integral Exponents
Linear Equations - Positive and Negative Slopes
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Basic Algebraic Operations and Simplification
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Axis of Symmetry and Vertices
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Evaluation of Simple Formulas
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Solving Linear Equations
Simple Trinomials as Products of Binomials
Solving Nonlinear Equations by Factoring
Solving System of Equations
Exponential Functions
Computing the Area of Circles
The Standard Form of a Quadratic Equation
The Discriminant
Dividing Monomials Using the Quotient Rule
Squaring a Difference
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Adding Fractions
Powers of Radical Expressions
Steps for Solving Linear Equations
Quadratic Expressions Complete Squares
Fractions 1
Properties of Negative Exponents
Factoring Perfect Square Trinomials
Solving Quadratic Equations Using the Square Root Property
Dividing Rational Expressions
Quadratic Equations with Imaginary Solutions
Factoring Trinomials Using Patterns
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Solving Linear Inequalities

An inequality can be formed by linking two expressions with an inequality symbol <, , >, or .

A linear inequality in one variable is an inequality that can be written in the form ax + b > c where a, b, and c are real numbers, a 0, x is a variable, and > may be replaced by , <, or .


Here are the definitions of the inequality symbols:

< means "less than", as in 4 < 5.

means "less than or equal to", as in 3 8 or 8 8.

> means "greater than", as in 6 > 1.

means "greater than or equal to", as in 2 0 or 2 2.

Here are some examples of linear inequalities:
3x < 18 -8w - 7 > 33 -7x - 13 ≤ -2(4x + 5)

A linear inequality can be solved using the same steps as when solving a linear equation, but with one important difference:

When you multiply or divide an inequality by a negative number, you must reverse the direction of the inequality symbol.

For example:

Reverse the inequality symbol.


-2x < 6

x > -3


When you divide into a positive number, do not reverse the inequality.


Example 1

Solve: -8w - 7 > 33. Then, graph the solution on a number line.


Add 7 to both sides.


Divide both sides by -8 and reverse the direction of the inequality symbol.


-8w - 7 > 33

-8w - 7 + 7 > 33 + 7

-8w > 40

w < -5


To graph the solution, plot an open circle on the number line at -5.

Then, shade the number line to the left of -5.


When graphing the solution of an inequality on a number line, remember the following:

• Use an open circle, °, if the inequality symbol is < or >.

An open circle indicates the point is NOT part of the solution.

• Use a closed circle, •, if the inequality symbol is or .

A closed circle indicates the point is part of the solution.

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