Solve for X: (X − 40.354/14.4) × 3562/3600 = (147.304 × 600 + 40.354 × 1492)/(14.4 × 3600).

Step-by-step solution

1. 1

   Evaluate the two constants on the left.

   $\frac{40.354}{14.4}=2.8023611111\ldots,\qquad \frac{3562}{3600}=0.9894444444\ldots$

   Both are exact rationals, so keeping them as fractions ($\tfrac{40354}{14400}$ and $\tfrac{1781}{1800}$) rather than truncated decimals avoids error accumulating through the division that follows.

2. 2

   Compute the numerator on the right, carefully.

   $147.304\times 600=88{,}382.4,\qquad 40.354\times 1492=60{,}208.168.$

   The second product is the one to double-check: $40.354\times1492=40.354\times1500-40.354\times8=60{,}531-322.832=60{,}208.168$. Their sum is

   $88{,}382.4+60{,}208.168=148{,}590.568.$

3. 3

   Compute the denominator and the right-hand value.

   $14.4\times 3600=51{,}840,\qquad \frac{148{,}590.568}{51{,}840}=2.8663304012\ldots$

4. 4

   Undo the multiplication. Divide both sides by $\tfrac{3562}{3600}$:

   $X-2.8023611111=\frac{2.8663304012}{0.9894444444}=2.8969088839.$

5. 5

   Undo the subtraction and state the exact value.

   $X=2.8969088839+2.8023611111=5.6992699950.$

   Carrying the whole computation in exact fractions gives $X=\dfrac{73{,}082{,}879}{12{,}823{,}200}$, whose decimal expansion is $5.699269995009\ldots$ — matching the decimal route to ten places. Note that mis-multiplying $40.354\times1492$ as $60{,}192.568$ (a common slip) would shift the right-hand side to $2.8653035$ and the answer to $5.6982309$, wrong in the third decimal.