4) $2 a =(-3 x +2\{- a +3 x -2|- a + b -(2+ a )|\})+3 x +8-4 b=$
5) $-4\{m-2 n-|3 n+2(2 n-m)+5(4 n-3 m)|\}+5(m-n)+67 m=$
6) $a-(a+b)-3\{-2 a+1-2 a+b+2(b-1)-a-b+1\}-3+7 b=$

Equation 1: Case 1: 2 a − 4 b + 3 x + 8 = 0 Case 2: 2 a − x = 0 Equation 2: Case 1: n = 0 Case 2: 136 m − 105 n = 0 Equation 3: a = 5 1 ​


Examples
Simplifying equations is a fundamental skill in algebra and has numerous real-world applications. For example, in physics, you might need to simplify equations to model the motion of objects or the behavior of electrical circuits. In economics, simplifying equations can help in analyzing market trends or predicting economic outcomes. In computer science, simplifying logical expressions is crucial for optimizing algorithms and ensuring efficient code execution.

Answered by GinnyAnswer | 2025-07-03

The simplifications for the equations yield multiple results: Equation 4 leads to two cases for a and b , Equation 5 gives conditions for n and m , and Equation 6 results simply in a = 5 1 ​ . The important step is analyzing the absolute values accurately for correct simplifications. Overall, you obtain functional expressions to work through based on the conditions set by the absolute values.
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Answered by Anonymous | 2025-07-04