Question

Розв'яжи рівняння 4 - |x - 4| > 1

Answer 1

х ∈ [1,7]

Х належить від 1 до 7 включно.

Answer 2

I can understand and communicate in Ukrainian. I will try to solve the equation for you.

The equation 4 - |x - 4| > 1 is an absolute value inequality. To solve it, we need to consider two cases: when x - 4 is positive and when x - 4 is negative.

Case 1: x - 4 > 0

In this case, we can remove the absolute value sign and get:

4 - (x - 4) > 1

Simplifying and rearranging, we get:

x < 7

Case 2: x - 4 < 0

In this case, we need to change the sign of x - 4 and reverse the inequality sign:

4 - (-(x - 4)) > 1

Simplifying and rearranging, we get:

x > 1

Combining the two cases, we get the final solution:

x > 1 or x < 7

You can check your answer by graphing the inequality on a number line or using an online calculator or .

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