RML MAINS 2025
Non Nursing Subjects
Hard
Solve: 5x + 3 = 7x + 9
Appeared in: RML MAINS 2025
Explanation
- The problem requires solving a linear equation to find the value of the variable 'x'.
- The core principle is to perform identical operations on both sides of the equation to isolate the variable.
- First, consolidate the 'x' terms on one side by subtracting 5x from both sides, resulting in 3 = 2x + 9.
- Next, consolidate the constant terms on the other side by subtracting 9 from both sides, resulting in -6 = 2x.
- Finally, solve for 'x' by dividing both sides by 2, which yields x = -3.
Why Other Options Were Wrong
- Option A: Substituting x = 3 into the equation gives 5(3) + 3 = 18 on the left and 7(3) + 9 = 30 on the right. Since 18 is not equal to 30, this option is incorrect.
- Option B: Substituting x = -6 into the equation gives 5(-6) + 3 = -27 on the left and 7(-6) + 9 = -33 on the right. Since -27 is not equal to -33, this option is incorrect. This error might occur if one incorrectly calculates 3 - 9 as 6 instead of -6 in an intermediate step.
- Option C: Substituting x = 5 into the equation gives 5(5) + 3 = 28 on the left and 7(5) + 9 = 44 on the right. Since 28 is not equal to 44, this option is incorrect.
Related Visual
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 this is a basic mathematics question, proficiency in algebra is a fundamental skill for nurses. It is essential for accurate calculations involving drug dosages, IV drip rates, body mass index (BMI), and interpreting various clinical data, all of which are critical for patient safety.
- Errors in basic math can lead to significant medication errors, potentially causing severe harm to patients. For example, miscalculating a decimal point or a variable can result in a tenfold overdose or underdose.
- What if? If the equation was part of a titration formula where 'x' is the rate adjustment needed, solving it incorrectly could lead to administering a medication too quickly or too slowly, failing to achieve the therapeutic goal or causing adverse effects.
How to Approach the Question
- First, identify the goal of the question, which is to 'Solve' the equation for the variable 'x'. This means you need to find the numerical value of 'x' that makes the equation true.
- Analyze the equation: 5x + 3 = 7x + 9. It's a linear equation with the variable 'x' on both sides.
- Formulate a plan. The standard strategy is to gather all terms containing the variable on one side of the equals sign and all constant terms (plain numbers) on the other side.
- Execute the plan systematically. Subtract 5x from both sides, then subtract 9 from both sides. This isolates the 'x' term.
- Perform the final step to solve for 'x'. In this case, divide by the coefficient of 'x' (the number next to it).
- Finally, check your answer by substituting the result back into the original equation to ensure the left side equals the right side.
Concept Tested & Keywords
- Concept Tested: Solving a first-degree linear equation with one variable.
- Stem keywords: Solve, equation, 5x + 3, 7x + 9
- Lead-in keywords: Solve
Question ID
QZh_2OQp3N5J-zF1LG3_6P
Practise the full RML MAINS 2025
Attempt every question from this paper in a timed mock, then review the full solution for each one.
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