Linear Equations in One Variable

SAT Math · Axiom Academy

Linear Equations in One Variable Master the fundamentals of solving equations In this lesson, you'll master the core techniques for solving equations: Isolating the variable using inverse operations Combining like terms and distributing Working with fractions and decimals This is the most common form you'll see on the SAT. Where: The Golden Rule of Solving Equations What you do to one side, you must do to the other. This keeps the equation balanced, like a scale with weights on both sides. Step 1: Simplifying Both Sides Distribute if needed: 2(x + 3) = 2x + 6 Step 2: Isolating the Variable Step 3: Working with Fractions Fractions can be tricky. Here's the key strategy: Strategy: Multiply to Eliminate Fractions When you see fractions, multiply every term by the LCD (least common denominator) to clear them. Step 4: Distributing and Combining Sometimes you need to distribute first, then combine like terms, then solve. Example: Solve 2(x + 3) - x = 12 Test with numbers: If you're unsure, plug in simple values to check your work. Work backwards: If you have answer choices, work backwards from them. Watch for signed numbers: The SAT loves negative numbers. Be careful with signs. Use clear notation: Show each step. It prevents careless mistakes. Your Equation-Solving Checklist Simplify both sides (distribute, combine like terms) Get all x-terms on one side, constants on the other Use inverse operations to isolate x Check by substituting back into the original equation

This is the written version of the interactive lesson above. See the full SAT Math course.