Solve the equation

Question

|y-4| = |y+10|

Answer 1

To solve the equation, we need to consider different cases based on the signs of y-4 and y+10.

Case 1: y-4 ≥ 0 and y+10 ≥ 0
In this case, the equation becomes y-4 = y+10.
Simplifying, we get -4 = 10, which is not true. Therefore, there is no solution in this case.

Case 2: y-4 < 0 and y+10 ≥ 0
In this case, the equation becomes -(y-4) = y+10.
Simplifying, we get -y + 4 = y + 10.
Combining like terms, we have 2y = -6.
Dividing both sides by 2, we get y = -3.

Case 3: y-4 ≥ 0 and y+10 < 0
In this case, the equation becomes y-4 = -(y+10).
Simplifying, we get y-4 = -y-10.
Adding y to both sides, we have 2y - 4 = -10.
Adding 4 to both sides, we get 2y = -6.
Dividing both sides by 2, we get y = -3.

Case 4: y-4 < 0 and y+10 < 0
In this case, the equation becomes -(y-4) = -(y+10).
Simplifying, we get -y + 4 = -y - 10.
Adding y to both sides, we have 4 = -10.
This is not true, so there is no solution in this case.

Therefore, the solutions to the equation |y-4| = |y+10| are y = -3.