Linear Equations
Lessons in this chapter
About Linear Equations
Linear Equations turns the expression skills from the previous chapter into the ability to actually solve for x, using the balance principle that whatever is done to one side of an equation must be done to the other.
Solve one-step linear equations in one variable introduces the balance idea with the simplest case: an equation like x + 7 = 15 or 4x = 20, where a single inverse operation (subtracting 7, or dividing by 4) isolates the variable in one move.
Solve multi-step linear equations in one variable builds directly on Algebraic Expressions’ combining-like-terms and distributive-property skills, working through equations like 3(x + 2) = 5x − 4 that need simplifying, distributing, combining like terms, getting all the variable terms on one side, before a single inverse operation can finish the job.
Both lessons in this chapter, Solve One-Step Linear Equations in One Variable and Solve Multi-Step Linear Equations in One Variable, are 7th grade math worksheets your child works through in the page. The questions are scored as they are answered, so the step where an equation stops balancing is visible immediately. Both are free to try, with no login needed for your first 3.
Frequently asked questions
Solve One-Step Linear Equations in One Variable comes first, undoing a single operation to isolate the variable while keeping both sides balanced. Solve Multi-Step Linear Equations in One Variable then stacks several of those steps together, usually combining like terms or distributing before the equation can be solved, which is exactly the toolkit the Algebraic Expressions chapter just built. This sits in the Common Core domain Expressions and Equations (7.EE).
A linear equation is a statement that two expressions are equal, where the variable appears only to the first power, no exponents. ‘Solving’ it means finding the one value of the variable that makes both sides equal, like finding that x = 8 is the only value that makes x + 7 = 15 true.
Whatever operation is done to one side of the equation has to be done to the other side too, or the two sides stop being equal. Kids picture this like a two-pan balance scale: add or remove the same weight from both sides and it stays level, exactly like solving an equation stays true when both sides get the same operation.
Use the inverse operation to undo whatever is being done to the variable, since 7 is being added in x + 7 = 15, subtract 7 from both sides to get x = 8. Solve One-Step Linear Equations in One Variable covers the addition/subtraction and multiplication/division versions of this same move.
Since x is being multiplied by 4, divide both sides by 4: 4x ÷ 4 = 20 ÷ 4, giving x = 5. The inverse of multiplication is division, the same pairing used for addition and subtraction.
A one-step equation needs exactly one inverse operation to isolate the variable. A multi-step equation needs more work first, distributing parentheses, combining like terms, or moving variable terms to one side, before it’s reduced down to that same simple one-step form.