Solving Linear Equations and Inequalities

If we carefully placed more rocks of equal weight on both sides of a balanced rock formation, it would still balance. Expressions in an equation behave the same way: they stay balanced as long as we do the same thing to both sides. This chapter builds up the tools for solving any linear equation, then extends the idea to formulas and to inequalities.

Sections

• Solve Equations Using the Subtraction and Addition Properties of Equality — verifying a solution, and undoing addition or subtraction.
• Solve Equations Using the Division and Multiplication Properties of Equality — undoing multiplication or division, including negative coefficients.
• Solve Equations with Variables and Constants on Both Sides — collecting variable terms on one side before solving.
• Use a General Strategy to Solve Linear Equations — a step-by-step strategy that handles any linear equation, plus classifying equations as conditional, an identity, or a contradiction.
• Solve Equations with Fractions or Decimals — clearing denominators and decimal points before solving.
• Solve a Formula for a Specific Variable — rearranging a formula to isolate one variable, including geometry and temperature formulas.
• Solve Linear Inequalities — graphing solutions on the number line, interval notation, and the one rule that flips an inequality.

This chapter overview is adapted from Elementary Algebra 2e, Chapter 2 Introduction by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, © OpenStax, licensed under CC BY-NC-SA 4.0. Access the original for free at openstax.org. Changes: condensed the chapter introduction and recast the chapter outline as a section list.