Solve the equation 8.8 - 10000x = 1010000x + 6.

Step-by-step solution

1. 1

   Collect the x terms on the side where the coefficient is larger. Adding $10000x$ to both sides keeps the coefficient positive and avoids a sign slip:

   $8.8 = 1010000x + 10000x + 6 = 1020000x + 6$

2. 2

   Move the constant across.

   $8.8 - 6 = 1020000x \quad\Longrightarrow\quad 2.8 = 1020000x$

3. 3

   Divide, keeping the exact fraction first.

   $x = \frac{2.8}{1020000} = \frac{28}{10200000} = \frac{7}{2550000}$

   Reducing before converting to a decimal avoids rounding a number this small too early.

4. 4

   Express in scientific notation.

   $x = \frac{7}{2550000} \approx 2.745098 \times 10^{-6}$

   The root is tiny precisely because the two $x$ coefficients did not cancel — they reinforced, summing to over a million, while the constants differed by only $2.8$.

5. 5

   Check by substitution. Left side: $8.8 - 10000(2.745098\times10^{-6}) = 8.8 - 0.02745098 = 8.77254902$. Right side: $1010000(2.745098\times10^{-6}) + 6 = 2.77254902 + 6 = 8.77254902$. The two agree to eight decimals.