Linear Equations

# SAT Math — Linear Equations ## What Linear Equations Questions Look Like Linear equation questions are among the most common math problems on the Digital SAT. They appear in the Math section — 2 modules × 35 minutes = 70 minutes total, 44 questions. The Math section is the second section on the SAT; it follows a 10-minute break after the Reading and Writing section. Most questions are multiple choice; some are Student-Produced Responses (SPR/grid-ins) requiring direct numerical entry. A built-in Desmos graphing calculator is available for both Math modules. Linear equations appear in Algebra content, which is one of the most heavily weighted Math content areas on the Digital SAT. A linear equation has the form: ax + b = c (no squared terms, no fractions with variables in the denominator). ## Solving Linear Equations: The Basics Goal: Get the variable alone on one side. Rule: Whatever you do to one side, do to the other. Example 1 (Simple): > 3x + 5 = 20 > Subtract 5: 3x = 15 > Divide by 3: x = 5 Example 2 (Variables on both sides): > 4x − 3 = 2x + 9 > Subtract 2x: 2x − 3 = 9 > Add 3: 2x = 12 > Divide by 2: x = 6 Example 3 (Distributive property): > 2(3x + 4) = 26 > Distribute: 6x + 8 = 26 > Subtract 8: 6x = 18 > Divide by 6: x = 3 ## Word Problems — Setting Up Equations This is where most students struggle. The key is translating…