Equations
Lessons in this chapter
About Equations
Equations builds directly on 7th grade's one- and multi-step equation work, extending it to equations with a variable on both sides and to rearranging real formulas.
Solving Simple Equations and Solving Multi-Step Equations review and extend the balance principle from 7th grade, using inverse operations, distributing, and combining like terms to isolate a variable, now with a faster pace since the underlying moves are already familiar.
Solving Equations with Variables on Both Sides is the genuinely new skill here: an equation like 5x + 3 = 2x + 12 has a variable term on each side, so the first move is always to combine those variable terms onto one side before solving as usual.
Rewriting Equations and Formulas closes the chapter by applying the same balance principle to real formulas, solving a formula like A = lw for w, for instance: the skill that lets a single formula be used to solve for whichever quantity is actually unknown.
All four lessons are 8th grade math worksheets worked inside the page, so Solving Multi-Step Equations, Solving Equations with Variables on Both Sides and Rewriting Equations and Formulas are sets of math problems rather than worked examples to read through. Each answer is marked as it is entered, so the step where the two sides stopped balancing is easy to find. The chapter is free to try, with no login needed for your first 3.
Frequently asked questions
Solving Simple Equations starts with one operation to undo, then Solving Multi-Step Equations stacks several of those steps and usually needs like terms combined or a bracket expanded first. Solving Equations with Variables on Both Sides adds the step of collecting the variable on one side, and Rewriting Equations and Formulas ends the chapter by solving a formula for a different letter, which is the skill every later volume and slope question depends on. This sits in the Common Core domain Expressions and Equations (8.EE).
7th grade covers one- and multi-step equations with a variable on one side; 8th grade's Equations chapter reviews both quickly before introducing the genuinely new skill: equations with a variable on both sides, and rewriting formulas for a different variable.
Move all the variable terms to one side and all the constant terms to the other, using inverse operations on both sides at each step, then solve the resulting one-step equation as usual: for 5x + 3 = 2x + 12, subtract 2x from both sides first to get 3x + 3 = 12.
It means solving the formula for a variable other than the one it’s usually written for: for example, starting with A = lw (area of a rectangle) and rearranging it to l = A/w, so the same formula can be used when the width and area are known but the length isn’t.
Combining variable terms incorrectly when moving them across the equal sign: for example, forgetting to also change the operation (from subtraction to addition, or vice versa) when a term moves from one side to the other.
Yes, if combining the variable terms cancels them out entirely, the equation reduces to either a false statement (no solution, like 3 = 5) or a true statement (infinitely many solutions, like 3 = 3), both real outcomes Solving Equations with Variables on Both Sides has kids recognize.