Solve  ∣∣y − 4∣∣=3.

The absolute value equation ∣∣y − 4∣∣ = 3 can be solved by setting up two separate equations, because the absolute value of a number can be either positive or negative.

1. y - 4 = 3
2. y - 4 = -3

Now, solve each equation separately:

For equation 1: y - 4 = 3 Add 4 to both sides to isolate y: y = 3 + 4 y = 7

For equation 2: y - 4 = -3 Add 4 to both sides to isolate y: y = -3 + 4 y = 1

So, the solutions to the equation ∣∣y − 4∣∣ = 3 are y = 7 and y = 1.