CLEP College Algebra

CLEP College Algebra covers fundamental algebraic concepts and skills necessary for success in college-level mathematics courses.

Algebraic Expressions and OperationsLinear Equations and InequalitiesFunctions and Their Graphs
Quadratic Equations and ApplicationsSystems of EquationsExponents, Radicals, and Rational Expressions
Algebra in Personal FinanceAlgebra in Science and TechnologyBusiness and Everyday Problem Solving
Mastering Multiple Choice QuestionsTime Management and Test-Taking Tips
Algebraic Expression...Linear Equations and...Functions and Their ...Quadratic Equations ...Systems of EquationsExponents, Radicals,...Algebra in Personal ...Algebra in Science a...Business and Everyda...Mastering Multiple C...Time Management and ...
Basic Concepts

Linear Equations and Inequalities

Solving Linear Equations

A linear equation is one where the variable is to the first power and appears in a straight line when graphed. The goal is to find the value of the variable that makes the equation true.

Steps to Solve

  1. Simplify each side of the equation.
  2. Move variable terms to one side and constants to the other.
  3. Isolate the variable by dividing or multiplying.

Working with Inequalities

Inequalities show relationships where values are greater than or less than each other, like \( x+3 > 7 \). The same steps as equations apply, but remember: when multiplying or dividing both sides by a negative, flip the inequality sign!

Graphing Solutions

Solutions to linear equations are points; solutions to linear inequalities are ranges, which can be shown on a number line.

Examples

  • Solve \( 2x - 5 = 9 \): Add 5 to both sides, then divide by 2 to get \( x = 7 \).

  • Solve \( 4x < 16 \): Divide both sides by 4 to get \( x < 4 \).

In a Nutshell

Linear equations and inequalities help us solve for unknowns and describe ranges of possible solutions.

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Functions and Their Graphs