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Chapter 17

1. $x < 0, y > 0$
2.
3. $\begin{array}{rcl} 3 x + 1 & < & - 5 \\ 3 x & < & - 6 \\ x & < & - 2 \end{array}$
4. $\begin{array}{rcl} - 1 & < & 1 - 2 x < 5 \\ - 2 & < & - 2 x < 4 \\ 1 & > & x > - 2 \\ - 2 & < & x < 1 \end{array}$

5. $\frac{x^{2} + x}{x - 2} \leq 0, \frac{x (x + 1)}{x - 2} \leq 0$

Interval	$\frac{x (x + 1)}{x - 2}$	Sign
$x < - 1$	$\frac{- -}{-}$	$-$
$- 1 < x < 0$	$\frac{- +}{-}$	$+$
$0 < x < 2$	$\frac{+ +}{-}$	$-$
$x > 2$	$\frac{+ +}{+}$	$+$

Solution: $x \leq - 1$ or $0 \leq x < 2$

A number line shaded to the left of a closed circle at negative 1, and shaded between a closed circle at 0 and open circle at 2.

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