Solve the equation 4.9725x + 0.68175 = 15.

Step-by-step solution

1. 1

   Undo the addition first. The $x$ term is multiplied, so the constant comes off before the coefficient does:

   $4.9725x = 15 - 0.68175 = 14.31825$

2. 2

   Divide by the coefficient.

   $x = \frac{14.31825}{4.9725}$

3. 3

   Clear the decimals to get an exact value. Multiplying numerator and denominator by $100000$ turns the quotient into $\tfrac{1431825}{497250}$. Dividing both by their greatest common divisor $1275$ gives

   $x = \frac{1123}{390}$

   Working exactly here matters: the quotient is a repeating decimal, and rounding the division too early is how the frequently seen (and wrong) value $2.8791$ arises.

4. 4

   Convert to a decimal.

   $x = \frac{1123}{390} = 2.879487179487\ldots \approx 2.879487$

   The block $487179$ repeats because $390 = 2 \times 3 \times 5 \times 13$ contains primes other than $2$ and $5$.

5. 5

   Check by substitution. $4.9725 \times 2.8794871795 = 14.31825000$, and adding $0.68175$ gives exactly $15$. Using the rounded $2.8791$ instead would give $14.316325 + 0.68175 = 14.998075$, off by nearly $2 \times 10^{-3}$.