Question

Which equation shows a valid, practical step in solving mc006-1.jpg?
mc006-2.jpg
mc006-3.jpg
mc006-4.jpg
mc006-5.jpg

Answer 1

I can’t see the images. Could you either paste the five equations here (type them out) or re-upload the images? Once I have the actual equations I’ll check which one is a valid/practical algebraic step and explain why.

If you want to check yourself in the meantime, here are quick ways to tell whether a suggested step is valid:

- Check that the transformation applied to both sides is an algebraically valid operation (add/subtract same thing, multiply/divide by nonzero, apply same function that’s one-to-one on the domain, etc.).
- Make sure you didn’t divide by an expression that could be zero (this can remove solutions).
- Beware non-equivalent operations like squaring both sides (can introduce extraneous roots) or canceling terms that aren’t common factors.
- Test the step by picking a value that satisfies the original equation and see whether it also satisfies the new equation (or pick several values).
- For steps like cross-multiplying, ensure denominators are nonzero before doing it.

Paste the equations and I’ll identify the correct step and explain why.