Solve for the given variable:

Question

5∣2n+8∣+3=33

Answer 1

We can start by subtracting 3 from both sides of the equation to isolate the absolute value term:

5∣2n + 8∣ = 30

Next, we can divide both sides of the equation by 5:

∣2n + 8∣ = 6

Now, we can split the equation into two cases, one with the positive value inside the absolute value and one with the negative value inside the absolute value:

Case 1: 2n + 8 = 6

Subtract 8 from both sides:

2n = -2

Divide both sides by 2:

n = -1

Case 2: -(2n + 8) = 6

First, distribute the negative sign:

-2n - 8 = 6

Add 8 to both sides:

-2n = 14

Divide both sides by -2:

n = -7

So, the two solutions for the given equation are n = -1 and n = -7.