Solve 1.8(X + 100) - X - 200 = 160.

Step-by-step solution

1. 1

   Expand the bracket. The $X$ inside the parentheses is multiplied by $1.8$, and so is the $100$: $1.8(X+100) = 1.8X + 180.$ The equation becomes $1.8X + 180 - X - 200 = 160$.

2. 2

   Combine the X-terms. $1.8X - X = 0.8X$, because the bare $-X$ has coefficient $1$. This is where a decimal subtraction is easy to fumble - write it as $1.8-1.0=0.8$.

3. 3

   Combine the constants. $180-200 = -20$, so the equation collapses to $0.8X - 20 = 160.$

4. 4

   Undo the subtraction. Add $20$ to both sides: $0.8X = 180.$

5. 5

   Divide by the coefficient. $X = \frac{180}{0.8} = \frac{1800}{8} = 225.$ Turning $0.8$ into the fraction $\tfrac45$ gives the same thing: $180 \cdot \tfrac54 = 225$.

6. 6

   Verify in the original equation. $1.8(225+100) = 1.8 \cdot 325 = 585$, then $585 - 225 - 200 = 160$ - exactly the right-hand side, so $X=225$ is correct.