solve the inequality : x^2 + 5x =< 24

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x^2 + 5x =< 24

First let us move 24 to the left side:

==> x^2 + 5x - 24 =< 0

Now let us factor :

==> (x+ 8) ( x-3) =< 0

Now we have two cases:

case (1):

(x+ 8) =< 0 AND (x-3) >= 0

==> x =< -8 AND x >= 3 ( no common solution)

case(2):

(x+ 8) >=0 AND (x-3) =< 0

==> x >- -8 AND x =< 3

Then ==> -8 =< x =< 3

**==> x belongs to the interval [ -8,3]**

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