Chapter A.9, Problem 102AYU

To determine

To express: The fact that $x$ differs from $-1$ by less than 1 as an inequality involving an absolute value. Solve for x.

Answer to Problem 102AYU

$\left\{x|-2 < x < 0\right\}\text{ or }\left(-2, 0\right)$

Explanation of Solution

$\begin{array}{l}|x - \left(-1\right)| < 1\hfill \\ |x + 1| < 1\hfill \\ -1 < x + 1 < 1\hfill \\ -1 - 1 < x + 1 - 1 < 1 - 1\hfill \\ -2 < x < 0\hfill \end{array}$

The solution set is $\left\{x|-2 < x < 0\right\}$ or using interval notation, all numbers in the interval $\left(-2, 0\right)$.