How do you solve compound inequalities 4x + 7 < 11 or 1 – x ≤ -2?

May 4, 2015

Initially treat the two inequalities separately

$4 x + 7 < 11$
$4 x < 4$
$x < 1$

$1 - x \le - 2$
$1 \le x - 2$
$3 \le x$

Combine as a compound condition
$4 x + 7 < 11 \text{ or } 1 - x \le - 2$
$\rightarrow$
$x < 1 \text{ or } x \ge 3$

$x \epsilon \left(- \infty , 1\right) \cup \left[3 , + \infty\right)$