Solve for X: 0.8X - 1200 = 320.

Step-by-step solution

1. 1

   Plan the two operations in reverse order. $X$ is first multiplied by $0.8$, then $1200$ is subtracted. Undoing works backwards: add $1200$ first, then divide by $0.8$.

2. 2

   Add 1200 to both sides.

   $0.8X=320+1200=1520$

3. 3

   Estimate before dividing. Dividing by $0.8$ makes a number larger by a quarter, so expect roughly $1520+380=1900$. Any answer smaller than $1520$ would signal that the operation went the wrong way.

4. 4

   Divide by 0.8 using the reciprocal. Since $\dfrac{1}{0.8}=1.25$:

   $X=\frac{1520}{0.8}=1520\times1.25=1900$

   Equivalently, clear the decimal first: $\dfrac{15200}{8}=1900$.

5. 5

   Verify in the original equation. $0.8\times1900=1520$, and $1520-1200=320$ ✓, matching the right side exactly and confirming the estimate of about $1900$ ✓.