Answer
a) $\{x |x \geq 3 \} \cap \{x|x< 6\}$
b) $\{x |x \gt -2 \} \cap \{x|x \lt5 \}$
Work Step by Step
a) $8 \leq x + 5 \lt 11$
$3 \leq x \lt 6$
The solutions of the inequality are given by $3 \leq x \lt 6$. We can write this as $x \geq 3$ and $x \lt 6$. This compound inequality is the intersection of two sets, which you can write as follows: $\{x |x \geq 3 \} \cap \{x|x< 6\}$
b) $|4x-6| \gt 14$
$-14 \lt 4x - 6 \lt 14$
Add 6 to each expression
$-8 \lt 4x \lt 20$
$-2 \lt x \lt 5$
The solutions of the inequality are given by $-2 \lt x \lt 5$. We can write this as $x \gt -2$ and $x \lt5$. This compound inequality is the intersection of two sets, which you can write as follows: $\{x |x \gt -2 \} \cap \{x|x \lt5 \}$
