Solve for x: x = 0.3 * 200 + 0.3x.

Step-by-step solution

1. 1

   Simplify the numeric term. $0.3\times200=60$, so

   $x=60+0.3x$

2. 2

   Gather the x terms before dividing. The unknown sits on both sides, so subtract $0.3x$:

   $x-0.3x=60\qquad\Longrightarrow\qquad (1-0.3)x=60\qquad\Longrightarrow\qquad 0.7x=60$

   What matters is the complement $1-0.3=0.7$, not the $0.3$ itself.

3. 3

   Divide by 0.7 and clear the decimal.

   $x=\frac{60}{0.7}=\frac{600}{7}$

   Multiplying top and bottom by $10$ gives the exact fraction; $7$ is prime and does not divide $600$, so it cannot be reduced.

4. 4

   Convert to a decimal.

   $\frac{600}{7}=85.714285\overline{714285}\approx85.71$

   The six-digit repeating block is characteristic of sevenths — a sign the fraction, not the decimal, is the right way to record the answer.

5. 5

   Sanity-check the size. The answer must exceed $60$ (since $0.3x>0$ is being added) but stay well below $200$. And $85.71$ is smaller than the $0.35$ case's $107.69$ and the $0.4$ case's $133.33$, which is right: a smaller multiplier means less self-reinforcement.

6. 6

   Verify by substitution. With $x=\tfrac{600}{7}$: the right side is $60+0.3\cdot\tfrac{600}{7}=60+\tfrac{180}{7}=\tfrac{420+180}{7}=\tfrac{600}{7}$ ✓ — exactly the left side.