Solve 31192041.56x + 31719594.84x + 24088814.72x = 99464.37 for x.

Step-by-step solution

1. 1

   Notice that every term on the left is a like term. Each contains $x$ to the first power, so the distributive property lets them be merged into a single coefficient. No expansion, substitution or system solving is needed — this is a one-step equation dressed up in large numbers.

2. 2

   Add the three coefficients.

   $31{,}192{,}041.56+31{,}719{,}594.84=62{,}911{,}636.40$

   $62{,}911{,}636.40+24{,}088{,}814.72=87{,}000{,}451.12$

   Adding in two stages keeps the decimal alignment checkable; all three values carry exactly two decimal places, so the sum must too.

3. 3

   Rewrite the equation in one-term form.

   $87{,}000{,}451.12\,x=99{,}464.37$

4. 4

   Divide both sides by the coefficient.

   $x=\frac{99{,}464.37}{87{,}000{,}451.12}=0.0011432627$

   The answer is small because the right side is roughly $10^5$ while the coefficient is roughly $8.7\times10^7$ — a ratio near $10^{-3}$, which is a useful order-of-magnitude check before doing the division.

5. 5

   Verify by substitution. $87{,}000{,}451.12\times0.0011432627=99{,}464.3700$, matching the right-hand side to four decimal places ✓. Keeping ten significant figures matters here: rounding $x$ to $0.00114$ would reproduce only $99{,}180$, an error of about \284$.