The equation: 5x + 2 = 10 + 3x

Appeared in: RML PRE 2025

Explanation

The goal is to isolate the variable 'x' on one side of the equation.
First, consolidate the 'x' terms by subtracting 3x from both sides: 5x - 3x + 2 = 10, which simplifies to 2x + 2 = 10.
Next, consolidate the constant terms by subtracting 2 from both sides: 2x = 10 - 2, which simplifies to 2x = 8.
Finally, solve for 'x' by dividing both sides by 2: x = 8 / 2, which results in x = 4.

Option A: Substituting x=5 gives 5(5)+2=27 on the left and 10+3(5)=25 on the right. Since 27 is not equal to 25, this is incorrect.
Option C: Substituting x=8 gives 5(8)+2=42 on the left and 10+3(8)=34 on the right. Since 42 is not equal to 34, this is incorrect.
Option D: Substituting x=12 gives 5(12)+2=62 on the left and 10+3(12)=46 on the right. Since 62 is not equal to 46, this is incorrect.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving a first-degree linear equation with one variable as background academic context rather than a clinical decision trigger.
While not a clinical question, strong foundational math skills are essential for safe nursing practice, particularly in medication dosage calculations.
Nurses frequently use formulas to calculate IV drip rates, drug titrations, and body surface area, all of which require accurately solving for an unknown variable.
What if the equation involved fractions or decimals, as is common in pediatric dosing? A mistake in isolating the variable could lead to a significant medication error, highlighting the need for precision.

How to Approach the Question

Identify the goal: The question asks to solve for the variable 'x'.
Scan the equation to see the terms involved: variable terms (5x, 3x) and constant terms (2, 10).
Apply the principle of balancing equations. Plan to group all 'x' terms on one side and all constant terms on the other.
Execute the steps: Subtract the smaller 'x' term (3x) from both sides. Then, subtract the constant term from the variable side.
Isolate 'x' by performing the final division.
Verify the answer by substituting your result back into the original equation to ensure both sides are equal.

Concept Tested & Keywords

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Practise the full RML PRE 2025

Attempt every question from this paper in a timed mock, then review the full solution for each one.