Solve the equation 0.8x - 400 = 240.

Step-by-step solution

1. 1

   Undo the subtraction. Add $400$ to both sides:

   $0.8x=240+400=640$

2. 2

   Rewrite $0.8$ as $\tfrac45$ and invert. Dividing by $\tfrac45$ means multiplying by its reciprocal $\tfrac54$:

   $x=640\cdot\frac{5}{4}$

3. 3

   Compute in the easy order. $640\div 4=160$, then $160\times 5=800$:

   $x=800$

   An equivalent shortcut: dividing by $0.8$ is multiplying by $1.25$, and $640\times 1.25=800$.

4. 4

   Verify. $0.8\times 800=640$ and $640-400=240$ $\checkmark$. As a sanity check on size, the coefficient is less than $1$, so $x$ must be larger than the right-hand side $640$ — and $800>640$ as expected.