Linear Equations from Word Problems
Most SAT word problems in the Algebra domain are a single linear equation in disguise. The arithmetic is short. The points leak in the translation: a relationship written backward, a rate turned upside down, or the answer reported a step early, when the item asked for the total and you gave one part.
These patterns aren't really about whether you can solve an equation. They're about whether you turned the words into the right equation, and whether you answered the question the test actually asked, not the one a step before it.
The work
4 ways in · any order
Lesson
Linear Equations from Word Problems
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Name the unknown, translate the relationship in the right direction, keep rates upright, then solve and report the exact quantity. The lesson works the method and the five patterns that derail it, and it saves the trap for last: the right number for a question the item never asked.
Diagnostic
10-item topic check
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Ten items across the five patterns: writing the relationship backward, flipping a rate, stopping at a middle step, answering for the wrong quantity, and a sign or side slip while solving. Take it cold to surface the ones still catching you, or after the lesson to confirm they are gone.
Grid-in Check
Student-produced response
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About a quarter of SAT math answers are typed, not chosen, with no options to react to. These grid-in items diagnose by the value you enter, then route into the same drills the multiple-choice check feeds.
Targeted Practice
Drill a single pattern
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Pick one of the failure modes you've missed and grind it on its own. The round is adaptive: two correct in a row clears the pattern and you move on.