Linear Equations
Lessons in this chapter
About Linear Equations
Linear Equations is where algebra starts answering questions, and the whole method rests on one principle: whatever you do to one side, do to the other.
Understand and Write Equations draws the line between an expression and an equation. An expression can be simplified; an equation states that two things are equal and can be solved. Writing one from a situation is the step that makes algebra useful.
Solve One-Step Addition and Subtraction Equations and Solve One-Step Multiplication and Division Equations teach undoing. To solve x + 7 = 12, subtract 7 from both sides; to solve 3x = 12, divide both sides by 3. The inverse operation is chosen by looking at what was done to the variable.
The balance idea is what keeps this honest. An equation is a statement that two sides weigh the same, and any operation applied to both sides preserves that, which is why the method works rather than being a rule to follow.
Solve Linear Equations in Two Variables and Graph Linear Equations in Two Variables extend to equations with x and y, where a solution is a pair rather than a single value. Plotting those pairs gives a straight line, which connects straight back to the ratio graphs earlier in the year.
Each of the five lessons in Linear Equations opens as a 6th grade math worksheet in the page. Solve One-Step Addition and Subtraction Equations, Solve One-Step Multiplication and Division Equations and Graph Linear Equations in Two Variables give practice questions worked one at a time and scored as you go. Free to try, with no login needed for your first 3.
Frequently asked questions
Understand and Write Equations draws the line between an expression and an equation, and makes solving mean finding the value that keeps both sides equal. Solve One-Step Addition and Subtraction Equations and Solve One-Step Multiplication and Division Equations then introduce the method, undoing the operation on both sides, which is the habit the whole of algebra is built on. Solve Linear Equations in Two Variables and Graph Linear Equations in Two Variables add a second variable, so a solution becomes a pair of values and the set of them becomes a line. The chapter sits in the Common Core domain Expressions and Equations (6.EE).
An expression like 3x + 5 can be simplified or evaluated. An equation like 3x + 5 = 20 states that two things are equal and can be solved.
Undo what was done to the variable, doing the same to both sides. For x + 7 = 12, subtract 7 from both sides to get x = 5.
Because an equation says the two sides are equal. Changing only one side breaks that, while changing both keeps it true, which is why the method works.
A pair of values, like x = 2 and y = 5, that makes the equation true. There are usually infinitely many, and plotting them gives a straight line.
Because the relationship changes at a constant rate. It is the same reason the ratio graphs earlier in the year were straight lines.