Answer
$(-∞,∞)$
Work Step by Step
$8(x+3 ) \lt 7(x+5) +x$
Applying distributive property,
$8x+24 \lt 7x+35 +x $
Combine like terms.
$8x+24 \lt 8x+35 $
Using addition property of inequality, add $-8x$ to both sides.
$8x+24 -8x \lt 8x+35-8x $
$24 \lt 35 $
This statement remains true for all values of $x$.
$x$ can be any real number.
Solution set in interval notation: $(-∞,∞)$