Solve the equation 4.9725x + 0.68175 = 20.

Step-by-step solution

1. 1

   Subtract the constant.

   $4.9725x = 20 - 0.68175 = 19.31825$

2. 2

   Divide by the coefficient.

   $x = \frac{19.31825}{4.9725}$

3. 3

   Turn it into an exact fraction. Multiplying top and bottom by $100000$: $\tfrac{1931825}{497250}$. Both are divisible by $25$, giving $\tfrac{77273}{19890}$, and $\gcd(77273, 19890) = 1$ since $19890 = 2 \times 3^2 \times 5 \times 13 \times 17$ and none of those primes divides $77273$. So

   $x = \frac{77273}{19890}$

4. 4

   Convert to a decimal.

   $x = \frac{77273}{19890} \approx 3.885018$

   More digits: $3.8850175968$.

5. 5

   Verify. $4.9725 \times 3.8850176 = 19.3182500$, and $19.31825 + 0.68175 = 20.00000$ exactly. Comparing with the same equation set to $15$, whose root is $2.879487$: raising the right-hand side by $5$ raised $x$ by $\tfrac{5}{4.9725} = 1.005531$, exactly the reciprocal of the slope.