Solve AND and OR compound inequalities — find the intersection or union of two solution sets, graph on a number line, and write in interval notation.
a ≤ x < b → [a, b)
AND means both conditions must be true simultaneously. You solve the three-part inequality by applying the same operations to all three parts at once.
The result is the intersection of both solution sets — typically a bounded interval between two values.
Special case: if the left bound ends up greater than the right bound after solving, the answer is No Solution (∅).
x < a OR x ≥ b → (−∞, a) ∪ [b, +∞)
OR means at least one condition is true. Solve each inequality independently, then take the union of both solution sets.
The graph typically shows two separate shaded regions, each extending to ±∞ on one side.
Special case: if the two regions overlap or touch, the solution is All Real Numbers (−∞, +∞).
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