4359 + 12.457 - __________ = 4200

Concept: In a linear equation of the form a + b - x = c, the unknown x is found by isolating it: adding or subtracting the same quantity keeps both sides of an equation equal, so moving x and the constant term across the equality gives x = (a + b) - c.

1. Write the given equation: 4359 + 12.457 - x = 4200.

2. Isolate x by moving it to the right-hand side and 4200 to the left-hand side: x = (4359 + 12.457) - 4200.

3. Add the two known values first: 4359 + 12.457 = 4371.457.

4. Subtract 4200 from this sum: 4371.457 - 4200 = 171.457.

Cross-check: substituting x = 171.457 back into the original equation confirms it - 4359 + 12.457 - 171.457 = 4200, so the equation holds true.

Hence, x = 171.457.