$832.58 - 242.31 = 779.84 - $ $x$

### Concept & Formula Rearrange the balancing equation components to construct an explicit linear solution path for the unknown algebraic variable $x$. $$ a - b = c - x \implies x = c - (a - b) \implies x = c - a + b $$ ### Step-by-Step Solution * Write down the primary mathematical statement: * $832.58 - 242.31 = 779.84 - x$ * Transpose $-x$ to the left to turn its value positive, moving left terms to the right: * $x = 779.84 - 832.58 + 242.31$ * Combine terms based on sign conventions: * $x = (779.84 + 242.31) - 832.58$ * Execute the positive additions: * $779.84 + 242.31 = 1022.15$ * Subtract the remaining parameter: * $x = 1022.15 - 832.58 = 189.57$ * Let's inspect choices: (a) $179.57$, (b) $199.57$, (c) $295.05$, (d) None of these. The exact value $189.57$ is absent, choosing (d). ### Exam Strategy & Shortcut **Fractional Balancing:** Evaluate decimal parts alone: $.58 - .31 = .27$. Right-side setup requires: $.84 - \text{decimal part} = .27 \implies \text{decimal part} = .84 - .27 = .57$. The correct option must end in $.57$, ruling out option (c). Estimate integer ranges: $832 - 242 = 590$. Now, $779 - x = 590 \implies x = 779 - 590 = 189$. Since $189.57$ isn't explicitly explicitly option (a) or (b), mark "None of these". ### Common Pitfall Students often compute $832.58 - 242.31 = 590.27$, then incorrectly add it to $779.84$ instead of subtracting it from $779.84$, leading to wildly inaccurate response targets. ### Final Answer **Therefore, the correct answer is None of these.**