Simplify the expression (x - 78000) * 0.055 + 1280.

Step-by-step solution

1. 1

   Recognise the shape. This is the standard bracket formula: a marginal rate $0.055$ applied to the amount above a threshold $78000$, plus a fixed base $1280$. Simplifying it turns a two-step rule into a single linear function $mx + b$.

2. 2

   Distribute the rate across the bracket.

   $(x - 78000)\cdot 0.055 = 0.055x - 78000 \times 0.055$

3. 3

   Evaluate the product exactly. Writing $0.055 = \tfrac{55}{1000}$ makes the arithmetic clean:

   $78000 \times \frac{55}{1000} = 78 \times 55 = 4290$

   Cancelling the three zeros before multiplying avoids a decimal-point error.

4. 4

   Combine the constants.

   $-4290 + 1280 = -3010$

5. 5

   Write the simplified form.

   $0.055x - 3010$

   The slope is unchanged at $0.055$, but the intercept is now explicit: the formula equals zero at $x = \tfrac{3010}{0.055} = 54{,}727.27$, and equals $1280$ exactly at the threshold $x = 78000$.

6. 6

   Check at two values. At $x = 78000$: original $= 0 + 1280 = 1280$; simplified $= 4290 - 3010 = 1280$. At $x = 100000$: original $= 22000(0.055) + 1280 = 1210 + 1280 = 2490$; simplified $= 5500 - 3010 = 2490$. Both agree.