In this aptitude (simplification and linear equations) question, solve for x in the decimal equation: 6.651 - (148.6 - x) - 57.22 = 6.098, being careful with the minus sign before the bracket and with decimal arithmetic.

Introduction / Context:
This problem is a linear equation in one variable with decimal coefficients. It is designed to test attention to detail with brackets, negative signs, and decimal subtraction. Although the algebra is not conceptually difficult, careless handling of signs or decimal places can easily lead to wrong answers.

Given Data / Assumptions:
We must solve 6.651 - (148.6 - x) - 57.22 = 6.098 for x.
All numbers are decimals in base ten and operations are standard addition and subtraction.

Concept / Approach:
The main idea is to remove the bracket carefully by distributing the minus sign, convert the equation into a simple linear form, and then isolate x. Combining like terms and handling decimal arithmetic correctly is crucial. We then check the candidate solution by substituting it back into the original equation.

Step-by-Step Solution:
Start from 6.651 - (148.6 - x) - 57.22 = 6.098. Distribute the minus inside the bracket: 6.651 - 148.6 + x - 57.22 = 6.098. Combine the constant terms on the left: 6.651 - 148.6 - 57.22. First, 6.651 - 148.6 = -141.949. Then -141.949 - 57.22 = -199.169. So the equation becomes x - 199.169 = 6.098. Add 199.169 to both sides to solve for x: x = 6.098 + 199.169 = 205.267.

Verification / Alternative check:
Substitute x = 205.267 back into the original equation. The bracket term becomes 148.6 - 205.267 = -56.667. Then 6.651 - (148.6 - x) - 57.22 becomes 6.651 - (-56.667) - 57.22, which equals 6.651 + 56.667 - 57.22. Summing 6.651 and 56.667 gives 63.318. Subtracting 57.22 yields 6.098, which matches the right hand side exactly. This confirms that x = 205.267 is correct.

Why Other Options Are Wrong:
Each incorrect option corresponds to typical mistakes. Option 218.569 may come from misadding decimals. Option 90.827 and 199.169 may arise from not isolating x properly or stopping mid way. The negative option is likely from sign errors while handling the bracket. None of these values satisfy the original equation when substituted back.

Common Pitfalls:
Learners often forget that subtracting a bracketed expression means changing the sign of each term inside. Another pitfall is misaligning decimal points during addition or subtraction. Writing down intermediate steps systematically and checking each numeric operation greatly reduces the risk of rounding or sign mistakes.

Final Answer:
The value of x that satisfies the equation is 205.267.