Solve 5|9 – 5n| – 7 = 38

Sure, let's solve the equation step by step.

First, let's simplify the equation by adding 7 to both sides:

5|9 – 5n| – 7 + 7 = 38 + 7

This simplifies to:

5|9 – 5n| = 45

Next, divide both sides by 5:

|9 – 5n| = 9

The absolute value of a number can be either positive or negative, so we can set up two equations:

9 - 5n = 9 and 9 - 5n = -9

Solving the first equation, 9 - 5n = 9, we subtract 9 from both sides:

-5n = 0

Then divide by -5:

n = 0

Solving the second equation, 9 - 5n = -9, we subtract 9 from both sides:

-5n = -18

Then divide by -5:

n = 18/5 = 3.6

So, the solutions to the equation are n = 0 and n = 3.6.