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

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Answer 1 · 2015-05-04T12:01:52

Initially treat the two inequalities separately

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

$1-x<=-2$
$1<=x-2$
$3<=x$

Combine as a compound condition
$4x+7<11 " or " 1-x<=-2$
$rarr$
$x<1 " or " x>=3$

$x epsilon (-oo,1) uu [3,+oo)$

How do you solve compound inequalities 4x + 7 < 11 or 1 – x ≤ -24x + 7 < 11 or 1 – x ≤ -2?