We have to determine the values of x that satisfy 2x^2 + 2x - 24 <= 0

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

divide both sides by 2

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

=> x^2 + 6x - 4x - 24 <= 0

=> x(x + 6) - 4(x + 6) <= 0

=> (x - 4)(x + 6) <= 0

This is true when either (x - 4)<= 0 and (x + 6) >=0 or when (x - 4)> = 0 and (x + 6)<=0

(x - 4)<= 0 and (x + 6) >=0

=> x <= 4 and x > = -6

The values of x satisfying this are [ -6, 4]

(x - 4)> = 0 and (x + 6)<=0

=> x >= 4 and x <= -6

There are no values that satisfy this.

**The solution of the given inequality lies in [-6, 4]**

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