The solution of the equation 4p - 2 = 10 is:

Appeared in: SGPGI Nursing Officer-2024

Explanation

The goal is to isolate the variable 'p' to find its value.
First, add 2 to both sides of the equation (4p - 2 = 10) to move the constant term to the right side. This results in 4p = 12.
Next, divide both sides by the coefficient of 'p', which is 4. This gives p = 12 / 4.
Simplifying the division gives the final answer, p = 3.

Option A: Substituting p=1 into the equation gives 4(1) - 2 = 4 - 2 = 2, which is not equal to 10. This error might occur from incorrectly subtracting 2 from 10 on the right side before adding it.
Option B: Substituting p=2 into the equation gives 4(2) - 2 = 8 - 2 = 6, which is not equal to 10. This error could happen if one incorrectly calculates 10 - 2 instead of 10 + 2 in the first step.
Option D: Substituting p=4 into the equation gives 4(4) - 2 = 16 - 2 = 14, which is not equal to 10. This error might occur if 12 was incorrectly divided by 3 instead of 4, or if 10 and 2 were added to get 12, and then 4 was added again.

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.
Accurate calculation is a fundamental skill in nursing, essential for tasks like medication dosage calculation, IV drip rate regulation, and interpreting patient data.
Errors in basic arithmetic can have severe consequences for patient safety, leading to underdosing or overdosing of critical medications.
What if? If a nurse miscalculated a dosage by a similar arithmetic error (e.g., confusing addition and subtraction), a patient could receive the wrong amount of medication, potentially causing harm or rendering the treatment ineffective.

How to Approach the Question

Identify the goal: to find the value of the variable 'p'.
Analyze the equation: It's a linear equation (4p - 2 = 10) with one unknown.
Use inverse operations to isolate 'p'. The operations on 'p' are subtraction (-2) and multiplication (4p).
First, undo the subtraction by performing the opposite operation, which is adding 2 to both sides of the equation.
Second, undo the multiplication by performing the opposite operation, which is dividing both sides by 4.
Perform the final calculation to find the value of 'p' and match it with the given options.

Concept Tested & Keywords

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