Solve 4x - 0.35(x - 1) = 220.45 for x.

Step-by-step solution

1. 1

   Distribute the bracket, minus sign included. The subtraction applies to both terms inside:

   $-0.35(x-1)=-0.35x+0.35$

   The constant comes out $+0.35$, not $-0.35$: two negatives make a plus. Missing this is the single most common error in this equation.

2. 2

   Combine the like terms.

   $4x-0.35x+0.35=3.65x+0.35$

   so the equation becomes $3.65x+0.35=220.45$.

3. 3

   Isolate the $x$ term.

   $3.65x=220.45-0.35=220.10$

4. 4

   Divide, keeping an exact fraction.

   $x=\frac{220.10}{3.65}=\frac{22010}{365}=\frac{4402}{73}$

   both parts having been scaled by $100$ and then divided by $5$. Since $73$ is prime and does not divide $4402$, the answer is not a terminating decimal.

5. 5

   Convert and check. $73\cdot 60=4380$ with remainder $22$, so $x=60+\frac{22}{73}=60.301370\ldots$ Substituting back: $3.65\cdot 60.301370=220.10$ and adding $0.35$ gives $220.45$. Note that the rounded $x=60.3$ would give $3.65\cdot 60.3+0.35=220.4450$, off in the third decimal — so $60.3$ is an approximation, not the solution.