Question

1. solve and check

\\(\frac{n - 31}{4} = 2\\)
answer:

Explanation:

Step1: Eliminate denominator (multiply by 4)

Multiply both sides by 4:
$$4 \times \frac{n-31}{4} = 2 \times 4$$
Simplify to get:
$$n - 31 = 8$$

Step2: Isolate variable n (add 31)

Add 31 to both sides:
$$n - 31 + 31 = 8 + 31$$
Simplify to get:
$$n = 39$$

Step3: Check solution (substitute n=39)

Substitute $n=39$ into original equation:
$$\frac{39-31}{4} = \frac{8}{4} = 2$$
This matches the right-hand side, so the solution is valid.

Answer:

$n=39$