SAT-Style: Absolute Value on the Number Line

SAT Math · Axiom Academy

Visual representation of absolute value problems The number line makes absolute value intuitive. Absolute value = distance, so we can literally draw the distance. Visualizing: Distance 5 from 3 Two solutions: x = -2 (5 units left of 3) and x = 8 (5 units right of 3) Visualizing: Within 3 units of -2 Solution: -5 < x < 1 (all x strictly between -5 and 1) Visualizing: At least 4 units from 1 Solution: OR (two separate regions) Key Insight: Interior vs Exterior Creates a RANGE (interior region between two points) : Creates TWO SEPARATE REGIONS (exterior, away from a point) → shaded in two directions (left and right) Draw it first: Sketch the number line even if the problem doesn't ask for it. Visual understanding helps. Closed vs open circles: use open circles. use closed circles. Remember distance is always positive: |x| = -5 has NO solutions because distance can't be negative. Double-check direction: Interior (between) vs exterior (away from). The inequality symbol tells you which.

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