Read off where one graph beats the other: To solve f(x) ≥ g(x), find where the graph of f is on or above g. The boundaries are the intersection points (where f = g) — then read off the x-intervals between them.
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IB-style question — solve graphically
Solve x² ≤ x + 2.
Step by step
- Intersections: set equal and solve.
- The parabola is below the line between these x-values.
Final answer
−1 ≤ x ≤ 2.
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Never multiply by something that could be negative: Move everything to one side, combine into a single fraction/expression, then use a sign analysis (number line of the critical points).
Don't cross-multiply a rational inequality — the denominator's sign can flip the direction.
IB-style question — rational inequality
Solve (x − 1)/(x + 2) ≥ 0.
Step by step
- Critical points: where the expression is 0 or undefined.
- Test each interval's sign on a number line.
- Keep where it's ≥ 0 (include x = 1, exclude x = −2).
Final answer
x < −2 or x ≥ 1.