Solve the inequation $5 (x - 2) > 4 (x + 3) - 24$ and represent its solution on a number line. Given the replacement set is $- 4, - 3, - 2, - 1, 0, 1, 2, 3, 4 .$

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Solution

$5 (x - 2) > 4 (x + 3) - 24$
$5 x - 10 > 4 x + 12 - 24$
$5 x - 4 x > - 12 + 10$
$x > - 2$
As the set $x$ is a sub-set of the replacement set ${- 4, - 3, - 2, - 1, 0, 1, 2, 3, 4,}$
set $x$ = ${- 1, 0, 1, 2, 3, 4,}$
Ans: The number of numbers in the set $x$ is 6

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