Linear equations in one variable

About this lesson

Linear equations in one variable: a standard solving routine, clearing fractions and parentheses without sign errors, no solution / infinitely many solutions with a constant, finding the requested expression directly, and setting up equations from word problems.

On the Digital SAT, linear equations in one variable are the foundation of the Algebra domain and often appear among the first questions of each math module. You may see an equation with parentheses and fractions, a question asking for the value of an expression like 2x − 3, an equation with a constant k that must have infinitely many solutions, or a word problem about rental or membership fees.

Because the skill feels easy, most lost points come from rushing: a minus sign that flips only one term, a fraction cleared without multiplying the right side, or a value of x given when the question wanted a different expression. This lesson sets out a fixed four-step routine, a table for counting solutions, a way to see when the expression you need is simply the left side scaled up or down, and backsolving and Desmos checks. It ends with 6 self-graded practice questions, each with a full explanation.