128k views
4 votes
Solve these equatins. Show solutions on a number line . |x-14|=14? please help asap

User Akhan
by
8.4k points

1 Answer

4 votes

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]-------->

User FoxyGio
by
7.7k points

Related questions

1 answer
24 votes
96.4k views