To solve the equation \( 1.26 (x - 7.352) = 6.326 \) for \( x \), follow these steps:
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Distribute the \( 1.26 \): \[ 1.26x - 1.26 \times 7.352 = 6.326 \] Calculate \( 1.26 \times 7.352 \): \[ 1.26 \times 7.352 \approx 9.25872 \] Thus, the equation becomes: \[ 1.26x - 9.25872 = 6.326 \]
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Add \( 9.25872 \) to both sides: \[ 1.26x = 6.326 + 9.25872 \] Calculate the right side: \[ 6.326 + 9.25872 \approx 15.58472 \] Now, the equation is: \[ 1.26x = 15.58472 \]
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Divide both sides by \( 1.26 \) to solve for \( x \): \[ x = \frac{15.58472}{1.26} \approx 12.398 \]
This value does not directly match the provided options. Let's check the calculations again:
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Recalculate for \( 6.326 + 9.25872 \):
The sum calculated earlier was approximate. Let's be more precise: \[ 6.326 + 9.25872 = 15.58472 \quad -> substituting back accurately \]
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Final Calculation for \( x \): \[ x = 12.39808 \text{ (this is close, but not directly matching the options)} \]
Given the options, let's see which one is nearest:
- 15.44876
- 15.038
- 12.452
- -2.525
The option "12.452" is closest to our computed value.
Thus, the best choice from the given options is: \[ \boxed{12.452} \]