\(-a < x < a\)
\(Given \leq\)
\(-a \leq x \leq a\)
\(Given: \,\, >\)
\(x > a\)
\(and\)
\(x < -a\)
\(Given: \,\, \geq\)
\(x \ge a\)
\(and\)
\(x \leq -a\)
\(ex. a\)See Part II: viewtopic.php?t=536
\(|x - 3| < 6\)
\(-6 <x - 3 < 6\)
\(-6 + 3 < x - 3 + 3 < 6 + 3\)
\(-3 < x < 9\)
\((-3, 9)\)
\(ex.\,\,b.\)
\(|5x + 10| \geq 6 \)
\(5x + 10 \geq 6 \)
\(5x + 10 - 10 \geq 6 - 10\)
\(5x \geq -4\)
\(\dfrac{5x}{5} \geq \dfrac{-4}{5}\)
\(x \geq -\dfrac{4}{5}\)
\(5x + 10 \leq -6 \)
\(5x + 10 - 10 \leq -6 - 10\)
\(5x \leq -16\)
\(\dfrac{5x}{5} \leq -\dfrac{16}{5}\)
\(x \leq -\dfrac{16}{5}\)
\((-\infty, -\dfrac{16}{5}] \cup [-\dfrac{4}{5}, \infty)\)
