Solve for the missing value in the linear relation: 3571 + ? − 6086 = 155

Difficulty: Easy

Correct Answer: 2670

Explanation:


Introduction / Context:
This linear arithmetic equation includes one unknown and a combination of addition and subtraction. The task is to isolate the unknown systematically, which reinforces the core principle that we can perform equal operations on both sides without changing the equality.


Given Data / Assumptions:

  • Equation: 3571 + ? − 6086 = 155
  • All numbers are integers.
  • We seek the exact integer value of the question mark.


Concept / Approach:
Group the constant terms from the left side to determine how much the unknown must contribute to reach the target on the right. Concretely, move 3571 and −6086 to the right as a combined constant, or combine them first on the left and then solve in one step.


Step-by-Step Solution:
1) Combine the known constants on the left: 3571 − 6086 = −2515.2) The equation becomes: ? − 2515 = 155.3) Add 2515 to both sides to isolate the unknown: ? = 155 + 2515.4) Evaluate: 155 + 2515 = 2670.


Verification / Alternative check:
Substitute: 3571 + 2670 − 6086 = 6241 − 6086 = 155, which verifies the solution.


Why Other Options Are Wrong:
2630: Gives 2630 − 2515 = 115, short by 40 from 155.2400: Gives 2400 − 2515 = −115, far from 155.2515: Confuses the magnitude; it would yield 0 on the reduced form, not 155.


Common Pitfalls:
Dropping a negative when combining 3571 and 6086, or mistakenly moving 6086 to the other side with the wrong sign. Writing the reduced equation ? − 2515 = 155 explicitly helps avoid errors.


Final Answer:
2670

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