Solve the decimal equation 3.352 − (9.759 − x) − 19.64 = 7.052 and find the value of x.

Introduction / Context:
This question is a straightforward but slightly lengthy decimal arithmetic problem. It tests your ability to handle brackets, negative signs, and decimal subtraction and addition accurately, which is important in many real life financial and data calculations.

Given Data / Assumptions:

• The equation is 3.352 − (9.759 − x) − 19.64 = 7.052.
• We must solve for x.
• All numbers are in decimal form and standard arithmetic rules apply.

Concept / Approach:
Main steps:

• Remove brackets carefully, noting that −(9.759 − x) changes signs.
• Combine like decimal terms on the left side.
• Isolate x on one side to obtain its value.
• Check the solution by substitution.

Step-by-Step Solution:
Start with 3.352 − (9.759 − x) − 19.64 = 7.052. Distribute the minus sign: 3.352 − 9.759 + x − 19.64 = 7.052. First combine 3.352 − 9.759 = −6.407. Then combine −6.407 − 19.64 = −26.047. So the equation becomes x − 26.047 = 7.052. Add 26.047 to both sides: x = 7.052 + 26.047. Compute the sum: 7.052 + 26.047 = 33.099. Therefore x = 33.099.

Verification / Alternative check:
Substitute x = 33.099 into the original equation: 3.352 − (9.759 − 33.099) − 19.64. Compute inside the bracket: 9.759 − 33.099 = −23.34. Then 3.352 − (−23.34) − 19.64 = 3.352 + 23.34 − 19.64 = 26.692 − 19.64 = 7.052. Since the left side equals the right side, the solution is correct.

Why Other Options Are Wrong:
Option a: −6.181 would give a very different value when substituted back, not equal to 7.052.
Option b: 13.581 is too small and does not balance the equation.
Option d: 39.803 is too large and leads to a left hand side much bigger than 7.052.
Option e: 3.099 is far from the correct sum and fails the substitution check.

Common Pitfalls:
Common mistakes include mishandling the minus sign before the bracket, incorrectly subtracting decimals, or rounding too early. To avoid these errors, perform operations systematically and line up decimal points carefully if doing manual arithmetic.

Final Answer:
The solution to the equation is x = 33.099.