Answer
$(-∞,-1)$
Work Step by Step
$5x-8 \lt 2(2+x) \lt -2(1+2x)$
Using Distributive property,
$5x-8 \lt 4+2x \lt -2-4x$
We can write it as
$5x-8 \lt 4+2x $ and $4+2x\lt -2-4x$
Using inequality properties, solving left hand side,
$5x-8 \lt 4+2x $
Add $-2x$ at both sides
$5x-8-2x \lt 4+2x -2x$
$3x-8 \lt 4$
Add $8$ at both sides
$3x-8+8 \lt 4+8$
$3x \lt 12$
Divide by $3$
$x \lt 4$
Solving at right hand side,
$4+2x\lt -2-4x$
Add $4x$ at both sides
$4+2x+4x \lt -2-4x+4x$
$4+6x\lt -2$
Add $-4$ at both sides
$4+6x-4\lt -2-4$
$6x\lt -6$
Divide by $6$
$x\lt -1$
$5x-8 \lt 4+2x $ and $4+2x\lt -2-4x$
$x \lt 4$ and $x\lt -1$
In interval notation: $(-∞,-1)$
