Question

Given: 3x-2<2x+1

Choose the solutions set:

A. x∈R|x<5
B. x∈R|x>-1
C. x∈R|x>1
D. x∈R|x<3

Answer 1

To solve the inequality 3x-2<2x+1, subtract 2x from both sides, then add 2 to both sides to isolate x. The correct solution set is x<3.

Step-by-step explanation:

To solve the inequality 3x-2<2x+1, we need to isolate the variable x. Here's how:

1. Subtract 2x from both sides of the inequality: 3x-2 - 2x < 2x+1 - 2x. This simplifies to x-2 < 1.
2. Add 2 to both sides of the inequality: x-2 + 2 < 1 + 2. This simplifies to x < 3.

Therefore, the solution set is x < 3. Choice D, x∈R|x<3, is the correct answer.