College Algebra

College Algebra covers fundamental algebraic concepts, including functions, equations, and inequalities, essential for higher-level mathematics.

Algebraic Expressions and OperationsSolving Equations and InequalitiesFunctions and Their Properties
Quadratic Equations and ApplicationsExponential and Logarithmic FunctionsSystems of Equations
Budgeting and Personal FinanceScience and Engineering ModelsBusiness and Economics
Practice and Review RegularlyBreak Down Complex Problems
Algebraic Expression...Solving Equations an...Functions and Their ...Quadratic Equations ...Exponential and Loga...Systems of EquationsBudgeting and Person...Science and Engineer...Business and Economi...Practice and Review ...Break Down Complex P...
Basic Concepts

Solving Equations and Inequalities

Unlocking the Unknown

Equations are statements that two things are equal (\(x + 2 = 5\)), while inequalities show how two expressions relate (\(x > 3\)). Solving them means finding all values that make the statement true.

Steps to Solve

  1. Isolate the variable using opposite operations (add, subtract, multiply, divide).
  2. For inequalities, remember to flip the sign when multiplying or dividing by a negative number.

Visualizing Solutions

  • Equations often have one solution, but inequalities can have many—represented as intervals on a number line.

Practical Importance

From calculating tips to setting budgets, equations and inequalities help solve everyday problems.

Examples

  • Solve \(3x - 7 = 11\): Add 7 to both sides (\(3x = 18\)), then divide by 3 (\(x = 6\)).

  • Solve \(2y + 5 > 11\): Subtract 5 (\(2y > 6\)), then divide by 2 (\(y > 3\)).

In a Nutshell

Solving equations and inequalities means finding values that make mathematical statements true.

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Functions and Their Properties