Solve the equation: -5x -2 = 3x + 10

Appeared in: RML PRE 2025

Explanation

The core task is to solve a linear equation by isolating the variable 'x'.
To begin, group like terms. Add 5x to both sides, resulting in -2 = 8x + 10.
Next, group the constant terms by subtracting 10 from both sides, which gives -12 = 8x.
Finally, solve for x by dividing both sides by 8, yielding x = -12/8.
Simplifying the fraction -12/8 gives -3/2, which is equal to -1.5.

Option A: Substituting x = 6 into the equation gives -5(6) - 2 = -32 on the left side and 3(6) + 10 = 28 on the right side. Since -32 is not equal to 28, this option is incorrect.
Option B: Substituting x = 5 into the equation gives -5(5) - 2 = -27 on the left side and 3(5) + 10 = 25 on the right side. Since -27 is not equal to 25, this option is incorrect.
Option C: Substituting x = 6.5 into the equation gives -5(6.5) - 2 = -34.5 on the left side and 3(6.5) + 10 = 29.5 on the right side. Since -34.5 is not equal to 29.5, this option is incorrect.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solving a linear equation with one variable as background academic context rather than a clinical decision trigger.
While this is a general mathematics question, the underlying skill is crucial in nursing for accurate medication dosage calculations.
Nurses frequently use formulas to calculate IV drip rates, drug concentrations, and patient-specific doses. A mistake in basic algebra can have serious patient safety consequences.
What if? If the equation involved fractions or decimals, as often happens in medication calculations (e.g., administering 2.5 mg from a solution of 5 mg/2 mL), the same principles of isolating the variable would apply, reinforcing the need for strong foundational math skills.

How to Approach the Question

First, identify the type of question. This is a straightforward algebra problem requiring you to solve a linear equation.
The goal is to isolate the variable 'x'. To do this, you need to perform the same operation on both sides of the equation to maintain the balance.
Decide which side to move the variable terms to and which side to move the constant terms to. A common strategy is to make the 'x' term positive. In this case, adding 5x to both sides achieves this.
Combine the like terms (all the 'x' terms together and all the constant numbers together).
Perform the final division or multiplication to solve for 'x'.
As a final check, substitute your answer back into the original equation to ensure both sides are equal.

Concept Tested & Keywords

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