The solution of the equation 12p - 11 = 13 is:

Appeared in: SGPGI Nursing Officer-2024

Explanation

The question asks for the solution to the linear equation 12p - 11 = 13.
The goal is to isolate the variable 'p'. The first step is to add 11 to both sides of the equation to cancel out the -11 on the left side.
This results in 12p = 13 + 11, which simplifies to 12p = 24.
The final step is to divide both sides by 12 to solve for 'p'.
This gives p = 24 / 12, which equals 2.

Option A: If p = 1, substituting it into the equation gives 12(1) - 11 = 12 - 11 = 1. This does not equal 13, so it is incorrect.
Option C: If p = 3, substituting it into the equation gives 12(3) - 11 = 36 - 11 = 25. This does not equal 13, so it is incorrect.
Option D: If p = 4, substituting it into the equation gives 12(4) - 11 = 48 - 11 = 37. This does not equal 13, so it is incorrect.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving a simple linear equation with one variable as background academic context rather than a clinical decision trigger.
While this is a mathematics question, basic algebra is a fundamental skill for nurses, essential for accurate medication dosage calculations, determining IV drip rates, and interpreting patient data.
For example, a nurse uses a simple algebraic equation to calculate the correct number of tablets to administer if a doctor orders 500mg of a drug and the available tablets are 250mg each (250x = 500, so x=2).
Accurate calculations are critical for patient safety and prevent medication errors.

How to Approach the Question

First, identify the type of question. This is a straightforward algebra problem asking to solve a linear equation.
Identify the goal: Find the value of the variable 'p' that makes the equation true.
Analyze the equation (12p - 11 = 13). Notice that 'p' is multiplied by 12, and then 11 is subtracted. To solve for 'p', you must reverse these operations.
Apply the principle of inverse operations. The opposite of subtracting 11 is adding 11. Add 11 to both sides to maintain the equality: 12p = 24.
Apply the next inverse operation. The opposite of multiplying by 12 is dividing by 12. Divide both sides by 12 to isolate 'p': p = 2.
Finally, check your answer by substituting p=2 back into the original equation: 12(2) - 11 = 24 - 11 = 13. The equation holds true, confirming the answer is correct.

Concept Tested & Keywords

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