Question

-2<=4-11х<=7 помогите

Answer 1

-2-4≤4-11х-4≤7-4
-6≤-11х≤3 (:(-11)
6/11≥x≥-3/11
x∈ [-3/11;6/11]

Answer 2

Solving the Inequality -2 <= 4 - 11x <= 7

To solve the inequality -2 <= 4 - 11x <= 7, we can first simplify it by solving the two separate inequalities it represents.

1. Solving -2 <= 4 - 11x: - Subtract 4 from both sides: -6 <= -11x - Divide by -11 (note that dividing by a negative number reverses the inequality): 6/11 >= x

2. Solving 4 - 11x <= 7: - Subtract 4 from both sides: -11x <= 3 - Divide by -11 (again, reversing the inequality): x >= -3/11

So, the combined solution for the inequality -2 <= 4 - 11x <= 7 is: -6/11 <= x <= -3/11.

This means that the values of x that satisfy the original inequality lie within the range from -6/11 to -3/11, inclusive.

Checking the Solution

Let's check the solution by substituting some values of x within this range back into the original inequality to ensure it holds true.

- When x = -6/11: - -2 <= 4 - 11*(-6/11) <= 7 - -2 <= 4 + 6 <= 7 - -2 <= 10 <= 7 (This is not true, so x = -6/11 is not a solution)

- When x = -3/11: - -2 <= 4 - 11*(-3/11) <= 7 - -2 <= 4 + 3 <= 7 - -2 <= 7 <= 7 (This is true, so x = -3/11 is a solution)

Based on this check, the solution -6/11 <= x <= -3/11 is correct.

Conclusion

The solution to the inequality -2 <= 4 - 11x <= 7 is -6/11 <= x <= -3/11.