Question

lise, Jake, Malik, and Xiao each solved the same inequality.

Elise’s Work Jake’s Work Malik’s Work Xiao’s Work

mc025-1.jpg

mc025-2.jpg
mc025-3.jpg

no solution mc025-4.jpg
all real numbers

Whose work is correct?
Elise’s work
Jake’s work
Malik’s work
Xiao’s work

Answer 1

I can’t see the images you referenced. Could you either

- paste the original inequality and each person’s work (or just their final answer), or
- upload the four images,

and I’ll check which solution is correct.

If you want to check quickly yourself, here are two fast ways:

1) Plug-in test values. Pick several values for the variable (especially near any critical points from denominators/zeros) and see which students’ answers are consistent with the original inequality. If a student’s solution says “all real numbers,” every test value must make the inequality true; if it says “no solution,” every test value must make it false.

2) Algebra check. Get everything on one side (0 on the other), combine into a single rational expression if needed, factor numerator and denominator, find sign-change points (zeros and undefined points), and test sign of each interval. Remember to flip the inequality sign when you multiply/divide by a negative and that squaring both sides can introduce extraneous solutions unless you handle cases carefully.

Send the inequality (and the four works) and I’ll identify which student is correct with a step-by-step check.