6x^-54≤0

Question 1

Задача Задача №66907

А

Аноним

28 ноября 2023 13:56 · публичный вопрос

А

Аноним 28 ноября 2023 13:56

6x^-54≤0

Answer

To solve the inequality 6x^(-54) ≤ 0, we need to consider two cases: when x > 0 and when x < 0.

Case 1: x > 0 In this case, x is positive and x^(-54) is also positive. So, multiplying a positive number by a positive number will always give a positive result. Therefore, there is no solution for this case.

Case 2: x < 0 In this case, x is negative and x^(-54) is positive. So, multiplying a negative number by a positive number will give a negative result.

Now, let's solve the inequality for x < 0.

6x^(-54) ≤ 0 Divide both sides of the inequality by 6: x^(-54) ≤ 0/6 x^(-54) ≤ 0

Since x is negative, we can rewrite the inequality as: 1/x^54 ≤ 0

The expression 1/x^54 will be positive for all nonzero values of x, since we are taking the reciprocal of x^54. Therefore, there is no solution for this case as well.

In conclusion, there are no solutions to the inequality 6x^(-54) ≤ 0, regardless of the value of x.

Question 2

6x^-54≤0

Answer

To solve the inequality 6x^(-54) ≤ 0, we need to consider two cases: when x > 0 and when x < 0. Case 1: x > 0 In this case, x is positive and x^(-54) is also positive. So, multiplying a positive number by a positive number will always give a positive result. Therefore, there is no solution for this case. Case 2: x < 0 In this case, x is negative and x^(-54) is positive. So, multiplying a negative number by a positive number will give a negative result. Now, let's solve the inequality for x < 0. 6x^(-54) ≤ 0 Divide both sides of the inequality by 6: x^(-54) ≤ 0/6 x^(-54) ≤ 0 Since x is negative, we can rewrite the inequality as: 1/x^54 ≤ 0 The expression 1/x^54 will be positive for all nonzero values of x, since we are taking the reciprocal of x^54. Therefore, there is no solution for this case as well. In conclusion, there are no solutions to the inequality 6x^(-54) ≤ 0, regardless of the value of x.