Solving Basic Linear Equations

A linear equation is an equation where the variable (usually x) appears only to the first power — no x^2, no sqrt{x}, no frac{1}{x}. The simplest form is: [formula] where a, b, and c are constants. Your goal: find the value of x that makes the equation true. The golden rule: whatever you do to one side, you must do to the other side. This keeps the equation balanced.

Some equations only need one operation to solve. Addition/Subtraction: If something is added to x, subtract it from both sides. If something is subtracted from x, add it to both sides. Multiplication/Division: If x is multiplied by a number, divide both sides by that number. If x is divided by a number, multiply both sides by that number.

Example: Solve x + 7 = 12

Many equations need two operations to solve. The strategy is: 1. First, undo addition or subtraction (move the constant) 2. Then, undo multiplication or division (isolate x) Think of it as peeling off layers — you remove them in reverse order.

Example: Solve 2x + 5 = 13

Basic linear equations are among the easiest SAT questions and appear early in each module. They are free points — solve them quickly and accurately to save time for harder problems. Always check your answer by plugging it back in.