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:

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