Solving Linear Equations
Lessons in this chapter
About Solving Linear Equations
Solving Linear Equations reviews and extends the equation-solving skills built across 7th and 8th grade, adding absolute value equations as a genuinely new case.
Solving Simple Equations and Solving Multi-Step Equations and Solving Equations with Variables on Both Sides review the full progression of equation-solving skills from middle school: one inverse operation, several combined steps, and variables appearing on both sides, at Algebra 1's faster pace.
Solving Absolute Value Equations introduces the one genuinely new idea: since |x| represents a distance from zero, an equation like |x - 3| = 5 has two possible solutions, one where x - 3 equals 5 and one where it equals -5, both needing to be solved and checked.
Rewriting Equations and Formulas closes the chapter by applying the same balance principle to real formulas, isolating whichever variable a problem actually calls for.
Every lesson in this chapter opens as an Algebra 1 worksheet inside the page, from Solving Simple Equations through Solving Absolute Value Equations and Rewriting Equations and Formulas. Each question is marked as you answer it, so a dropped negative or a missed second case shows up straight away instead of at the end of a page of work. Algebra 1 is the 9th grade course in most U.S. schools, so this is usually where algebra for 9th graders starts, and all five worksheets are free to practice online.
Frequently asked questions
Solving Simple Equations, Solving Multi-Step Equations and Solving Equations with Variables on Both Sides come first, reviewing the whole equation-solving progression from 7th and 8th grade at Algebra 1 pace. Solving Absolute Value Equations then adds the one genuinely new idea, that |x| is a distance from zero, so an equation like |x-3|=5 has two solutions that both have to be set up and checked. Rewriting Equations and Formulas closes the chapter by applying the same balance principle to real formulas. All five lessons sit in the high school Algebra conceptual category (A).
Absolute value equations are the genuinely new addition, since |x| represents distance from zero, an equation like |x-3|=5 has two solutions, requiring both cases to be set up and solved.
Isolate the absolute value expression, then split into two separate equations: one where the inside equals the positive value, one where it equals the negative, and solve each.
Solving only one of the two cases and stopping, since |x-3|=5 truly has two valid solutions (x=8 and x=-2), missing the negative case misses half the answer.
Yes, since absolute value can never be negative, an equation like |x-3|=-5 has no solution at all, because no value could ever make the left side negative.
Combine all variable terms onto one side and all constant terms onto the other using inverse operations on both sides, then solve the resulting simple equation.