I have tried it for multiple times but it still doesn’t work TvT! Please help me eight this question

  a) x = -2

  b) 8 integer values

Step-by-step explanation:

Matthew's solution is correct as far as it goes. However, he failed to take into account the possibility of negative square roots.

His solution might rightly look like ...

  3 < 3x² ≤ 75

  1 < x² ≤ 25 . . . . . divide by 3

  1 < ±x ≤ 5 . . . . . . take the square root

Separating the results:

  1 < x ≤ 5

  -1 > x ≥ -5 . . . . . . multiply by -1

The value x=-2 shows Matthew's solution is incorrect:

  3 < 3(-2)² ≤ 25   ⇒   3 < 12 ≤ 25 . . . true

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x can have the integer values {-5, -4, -3, -2, 2, 3, 4, 5}, a total of 8 values.

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In the attached, the white space (and dashed line) are the solution set. The shaded areas (and solid line) are excluded from the solution set.

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Additional comment

It can be helpful to remember that ...

That is, values of x may be negative, but the positive square root will only show you a positive value.

f(x) = -x -3

Step-by-step explanation: