Question

equation: 312 = 52n; inverse operation: (blank); solution: (blank); check: (blank)

Explanation:

Step1: Identify Inverse Operation

The equation is \(312 = 52n\), which is a multiplication equation (\(n\) is multiplied by 52). The inverse operation of multiplication is division. So we will divide both sides by 52.

Step2: Solve for \(n\)

Divide both sides of the equation \(312 = 52n\) by 52:
\(\frac{312}{52}=\frac{52n}{52}\)
Simplify both sides: \(6 = n\) (since \(312\div52 = 6\) and \(\frac{52n}{52}=n\)).

Step3: Check the Solution

Substitute \(n = 6\) back into the original equation \(312 = 52n\):
Right - hand side: \(52\times6=312\)
Left - hand side: \(312\)
Since the left - hand side equals the right - hand side, the solution is correct.

Answer:

• Inverse Operation: Division (Divide both sides by 52)
• Solution: \(n = 6\)
• Check: Substitute \(n = 6\) into \(312 = 52n\), \(52\times6 = 312\), which matches the left - hand side, so the solution is correct.