Linear Equations

Linear equations are one of the most fundamental tools in algebra, and they show up everywhere on the SAT—sometimes on their own, sometimes hiding inside word problems or more complex questions. A linear equation in one variable is simply an equation where you're looking for the value of a single unknown (usually x) that makes the equation true. For example, "2*x + 5 = 13" is a linear equation: you need to find what number x must be so that when you double it and add 5, you get 13.

The beautiful thing about linear equations is that they follow consistent, logical rules. You're not guessing—you're systematically unwrapping the equation to isolate the variable, almost like peeling layers off an onion. By the end of this lesson, you'll be able to solve any linear equation the SAT throws at you, whether it's simple or dressed up with fractions, parentheses, or variables on both sides. You'll also understand why each step works, which means you won't just be following recipes—you'll actually know what you're doing.

Beyond just finding x, you'll learn to interpret what your answer means in context, catch the traps the test writers set, and work efficiently under time pressure. Let's build this skill from the ground up.