Solving Equations and Inequalities

Resources and Examples

General Resources

• Solving Equations and Inequalities, Paul's Online Notes
• Solving Equations and Inequalities, Khan Academy
• Rules for Solving Inequalities, Math Is Fun

Solving Different Types of Equations

• College Algebra from Lumen Learning:
  • Solving Linear Equations with One Variable
  • Solving Rational Equations
  • Solving Quadratic Equations by Factoring
  • Completing the Square to Solve Quadratic Equations
  • Using the Quadratic Formula
  • Solving Other Types of Equations (go through this section by clicking "next")
• Solving Absolute Value Equations, Cliff's Notes

Solving Different Types of Inequalities

• Solving Linear Inequalities, patrickJMT on YouTube
• Solving Quadratic Inequalities, patrickJMT on YouTube
• Solving Quadratic Inequalities: More Examples, patrickJMT on YouTube
• Solving Absolute Value Inequalities, patrickJMT on YouTube
• Solving Inequalities with Radicals, University of Michigan Math Prep

NOTE: The same methods for solving equations can be used for solving inequalities. However, multiplying or dividing by a negative number on both sides of an inequality reverses the inequality sign. Examples of this:

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -x < 7 \implies (-1)(-x) > (-1)(7) \implies x > -7 }
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 6 - y \ge x \implies y - 6 \le -x \implies y \le 6 - x}
• $-2x>24\implies (-2x)/(-2)<24/(-2)\implies x<-12$