Linear Equations
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Lesson overview
Solving single-variable linear equations quickly and checking your work.
Go to lesson quiz →Exam guidance · Digital SAT Adaptive-Module Lens
Pacing
~71s per Reading/Writing item; ~95s per Math item with built-in Desmos graphing calculator.
How SAT marks this
Module 1 accuracy unlocks the higher-ceiling Module 2; graph intersections in Desmos often beat manual algebra.
Watch out for
Solving for x instead of the expression requested in the final clause of the stem.
Lesson content
Overview — Linear Equations
Solving single-variable linear equations quickly and checking your work. This lesson is at the beginner level — by the end, you'll be able to recognise this question type, apply a reliable method, and avoid the traps that cost marks.
Key Concept
A linear equation in one variable can always be solved by isolating that variable through inverse operations, applied in reverse order of operations, until the variable stands alone on one side.
Why It's Tested This Way
College Board tests linear equations because they underlie nearly every other SAT Math topic — word problems, systems, and inequalities all reduce to this same isolation technique once set up correctly.
Method
Move all variable terms to one side and all constants to the other using addition or subtraction, then divide both sides by the variable's coefficient — and always substitute your answer back into the original equation to verify it.
Worked Example
Solve 3x + 7 = 22: subtract 7 from both sides to get 3x = 15, then divide by 3 to get x = 5. Checking: 3(5) + 7 = 22. ✓
Second Worked Example
Solve 2(x − 4) = 3x + 1: distribute to get 2x − 8 = 3x + 1, subtract 2x from both sides to get −8 = x + 1, then subtract 1 to get x = −9. Checking: 2(−9−4) = 2(−13) = −26, and 3(−9)+1 = −26. ✓
Common Traps
The classic trap is a sign error when distributing a negative or moving a term across the equals sign — always double-check that every term's sign flipped correctly, and verify your final answer by substitution rather than assuming your algebra was correct.
Lesson Summary
Remember: (1) identify what is being asked, (2) apply the SAT strategy, (3) check against the traps. Complete the 10-question quiz below to unlock the next lesson — you need at least 60% to pass.
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