Final answer:
The correct comparison of solutions for the given inequalities is x<2 and x>2, leading to an empty set solution.
Step-by-step explanation:
To solve the inequalities 2x+6<10 and -2x+_22<18, we will isolate the variable x and determine the value(s) that satisfy both inequalities.
- For the inequality 2x+6<10, we will subtract 6 from both sides to get 2x<4. Then, we divide both sides by 2 to get x<2.
- For the inequality -2x+_22<18, we will subtract _22 from both sides to get -2x<18-_22, which simplifies to -2x<-4. Dividing both sides by -2, we get x>2.
Therefore, the correct comparison of solutions is x<2 and x>2, which means that there are no values of x that satisfy both inequalities simultaneously. This is called an empty set solution, indicating that there is no solution for the system of inequalities.