Solve the equation 4x - 0.35(x - 1) = 253.586.

Step-by-step solution

1. 1

   Distribute −0.35 over both terms in the bracket. The second product is $(-0.35)(-1) = +0.35$:

   $4x - 0.35x + 0.35 = 253.586$

   Writing $-0.35$ there instead is the standard sign error and shifts the root by about $0.19$.

2. 2

   Combine the x terms.

   $4x - 0.35x = 3.65x \quad\Longrightarrow\quad 3.65x + 0.35 = 253.586$

3. 3

   Subtract the constant.

   $3.65x = 253.586 - 0.35 = 253.236$

4. 4

   Divide, keeping the exact value.

   $x = \frac{253.236}{3.65} = \frac{253236}{3650} = \frac{126618}{1825} \approx 69.379726$

   The fraction does not reduce further, so the decimal repeats rather than terminating — rounding to $69.38$ is fine for reporting but not for further calculation.

5. 5

   Check by substitution. $4(69.379726) = 277.518904$ and $0.35(68.379726) = 23.932904$; their difference is $253.586000$, matching the right-hand side exactly.