Solving Linear Equations in One Variable
Solving a linear equation comes down to keeping it balanced while you isolate the variable. The arithmetic is short. The points leak somewhere else: in the distribution, in a dropped sign, in combining terms that do not combine, and in stopping a step early when the item asked for 2x, not just x.
These patterns aren't really about whether you can solve an equation. They're about whether the same small move stays clean under time pressure, 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
Solving Linear Equations
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Balance, distribute, combine, isolate, then check what the item asked for. The lesson works the four moves and the five patterns that derail them, 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: distributing to only the first term, dropping a sign on a negative factor, combining unlike terms, changing one side only, and answering for x when the item wanted an expression. 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.