Solve the equation 0.8x - 100 = 160.

Step-by-step solution

1. 1

   Clear the constant term first. Add $100$ to both sides:

   $0.8x=160+100=260$

2. 2

   Turn the decimal coefficient into a fraction. Dividing by a decimal invites slips, and $0.8=\tfrac{4}{5}$, so dividing by $0.8$ is the same as multiplying by $\tfrac{5}{4}$:

   $x=260\cdot\frac{5}{4}$

3. 3

   Finish the arithmetic. Divide $260$ by $4$ first to keep the numbers small:

   $\frac{260}{4}=65,\qquad 65\times 5=325$

   so $x=325$.

4. 4

   Check in the original equation. $0.8\times 325=260$, and $260-100=160$ $\checkmark$. Because $0.8$ is exact in fraction form, this check involves no rounding at all.