Answer:
Explanation:
To solve the equation |x-14|=14, we consider two cases:
Case 1: (x-14) is positive or zero, i.e., x-14 ≥ 0, which implies x ≥ 14. In this case, we have:
|x-14| = x-14 = 14
Solving for x, we get:
x = 14 + 14 = 28
Therefore, x = 28 is a solution in this case.
Case 2: (x-14) is negative, i.e., x-14 < 0, which implies x < 14. In this case, we have:
|x-14| = -(x-14) = 14
Solving for x, we get:
-x + 14 = 14
-x = 0
x = 0
Therefore, x = 0 is a solution in this case.
Hence, the solutions to the equation |x-14|=14 are x = 0 and x = 28. We can show these solutions on a number line as follows:
<--------[0]--------(14)--------[28]-------->