What is wrong with the following equation? $4+(10 / 5)=6-2$
We are tasked with evaluating the equation \(4 + \left(\frac{10}{5}\right) = 6 - 2\) to determine its validity. We must follow the standard order of operations, which dictates that operations inside parentheses or division must be performed before addition. Similarly, we will perform the subtraction on the right-hand side.
First, we evaluate the left-hand side (LHS) of the equation: \(4 + \left(\frac{10}{5}\right)\).
Following the order of operations, we first perform the division within the parentheses: \(\frac{10}{5} = 2\).
Then, we add the result to 4: \(4 + 2 = 6\).
Thus, the left-hand side simplifies to \(6\).
Next, we evaluate the right-hand side (RHS) of the equation: \(6 - 2\).
Performing the subtraction directly: \(6 - 2 = 4\).
Thus, the right-hand side simplifies to \(4\).
Comparing the results, the LHS evaluates to 6 and the RHS evaluates to 4. Since \(6 eq 4\), the equation \(4 + \left(\frac{10}{5}\right) = 6 - 2\) is mathematically incorrect. The error lies in the assertion that these two expressions are equal when they yield different numerical values. Therefore, the equation is \(\boxed{\text{invalid}}\).
This exercise demonstrates the importance of verifying equations before accepting them as true. In fields like accounting or programming, errors in simple arithmetic or logic can lead to significant discrepancies. By breaking down expressions into their constituent parts—LHS and RHS—one can systematically identify errors, ensuring that budgets, algorithms, and data calculations remain accurate and reliable.