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

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:

• $-x<7\implies (-1)(-x)>(-1)(7)\implies x>-7$
• $6-y\geq x\implies y-6\leq -x\implies y\leq 6-x$
• 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 -2x > 24 \implies (-2x)/(-2) < 24/(-2) \implies x < -12 }

More Examples of Solving 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