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Inequalities can be read straight off a graph. Where one curve sits above another, the corresponding inequality holds. This turns a tricky algebra problem into reading intervals from a sketch.
What you'll be able to do
The statement is true for the -values where the graph of lies the graph of . Likewise is where is below .
The points where the two graphs cross are the boundaries of the solution intervals. Solve to find them, then decide which intervals satisfy the inequality.
Tip — Find the crossing points first — they always divide the x-axis into the candidate intervals.
Once you have the boundaries, a quick sketch (or testing a value in each interval) tells you which side the inequality holds.
Formula recap
Common mistakes to avoid
Key takeaways
Test yourself
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