Graphing inequalities
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For each inequality, state whether the boundary line should be solid or dashed when graphed, and explain why.
(a) \(y > 3x - 2\)
(b) \(y \leq x + 5\)
(c) \(y \geq -2x + 1\)
(d) \(y < \dfrac{1}{2}x\)
(a) y>3x-2: DASHED — strict inequality (>), boundary not included.
(b) y≤x+5: SOLID — non-strict (≤), boundary included.
(c) y≥-2x+1: SOLID — non-strict (≥), boundary included.
(d) y<(1/2)x: DASHED — strict inequality (<), boundary not included. Rule: < or > → dashed; ≤ or ≥ → solid.
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