3.3 Compound Inequalities

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Notes

A compound inequality joins two inequalities.

And: both must be true. $-2 < x \le 4$ is the overlap between $-2$ and 4.
Or: at least one must be true. $x < -1$ or $x > 3$ shades two separate pieces.
Solve "and" inequalities by doing the same thing to all three parts: $-3 \le 2x + 1 < 7 \Rightarrow -4 \le 2x < 6 \Rightarrow -2 \le x < 3$.

Solve $-1 < x - 4 < 6$.

Which number satisfies $x \le -2$ or $x > 5$?

Solve $\displaystyle 1 \le \frac{x}{2} + 3 \le 5$.