Solve 295 = x + 9.2 + (0.0152x)/(1 - 0.0152) for x.

Step-by-step solution

1. 1

   Recognise that the fraction is linear in $x$, not a new unknown. The term $\dfrac{0.0152x}{1-0.0152}$ has $x$ only in the numerator, so it is simply $x$ times a constant. That means the whole equation is linear and can be solved by collecting like terms — no cross-multiplication is needed.

2. 2

   Simplify the constant denominator.

   $1-0.0152=0.9848$

   so the fee term is $\dfrac{0.0152}{0.9848}\,x$. Dividing:

   $\frac{0.0152}{0.9848}=0.01543866...$

   Keep the exact fraction $\tfrac{0.0152}{0.9848}=\tfrac{152}{9848}=\tfrac{19}{1231}$ to avoid rounding drift.

3. 3

   Move the constant across and collect the $x$ terms. Subtract $9.2$ from both sides:

   $295-9.2=x\left(1+\frac{19}{1231}\right)$

   $285.8=\frac{1250}{1231}\,x$

   since $1+\tfrac{19}{1231}=\tfrac{1250}{1231}$.

4. 4

   Divide to isolate $x$.

   $x=285.8\cdot\frac{1231}{1250}=\frac{351,\!819.8}{1250}=281.45584$

   This is exact, not rounded — the fraction $\tfrac{1231}{1250}$ terminates.

5. 5

   Check by substituting back. With $x=281.45584$: the fee term is $0.0152\cdot 281.45584/0.9848=4.27812.../0.9848=4.34416$, and $281.45584+9.2+4.34416=295.00000$. The equation balances exactly, confirming $x=281.45584$.