To solve the equation \(0.2x - 2.15 = -8.27a - 1.224b - 30.6c - 3.06d - 52.1\), we first need to isolate \(x\).
Here's the process:
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Move all terms involving \(a\), \(b\), \(c\), and \(d\) to the left side: \[ 0.2x - 2.15 + 8.27a + 1.224b + 30.6c + 3.06d + 52.1 = 0 \]
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Rearranging gives: \[ 0.2x = 2.15 - 8.27a - 1.224b - 30.6c - 3.06d - 52.1 \]
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Now, simplify the constants on the right: \[ 0.2x = 2.15 - 52.1 - 8.27a - 1.224b - 30.6c - 3.06d \] \[ 0.2x = -49.95 - 8.27a - 1.224b - 30.6c - 3.06d \]
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Now, divide both sides by 0.2 to solve for \(x\): \[ x = \frac{-49.95 - 8.27a - 1.224b - 30.6c - 3.06d}{0.2} \]
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Simplifying this gives: \[ x = -249.75 - 41.35a - 6.12b - 153c - 15.3d \]
So, the solution for \(x\) in terms of \(a\), \(b\), \(c\), and \(d\) is: \[ x = -249.75 - 41.35a - 6.12b - 153c - 15.3d \]
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