The first problem asks us to find which of the given values of $x$ are solutions to the inequality $\frac{7x+6}{2} \le 3x+2$. The second problem asks us to find the solution set to the inequality $2x-3 > \frac{2x-5}{2}$.

1. Problem Description

The first problem asks us to find which of the given values of $x$ are solutions to the inequality $\frac{7x+6}{2} \le 3x+2$.

The second problem asks us to find the solution set to the inequality $2x-3 > \frac{2x-5}{2}$.

2. Solution Steps

Problem 1:

We need to check each value of $x$ to see if it satisfies the inequality.

A. $x=-3$: $\frac{7(-3)+6}{2} \le 3(-3)+2 \Rightarrow \frac{-21+6}{2} \le -9+2 \Rightarrow \frac{-15}{2} \le -7 \Rightarrow -7.5 \le -7$. This is true.

B. $x=-2$: $\frac{7(-2)+6}{2} \le 3(-2)+2 \Rightarrow \frac{-14+6}{2} \le -6+2 \Rightarrow \frac{-8}{2} \le -4 \Rightarrow -4 \le -4$. This is true.

C. $x=-1$: $\frac{7(-1)+6}{2} \le 3(-1)+2 \Rightarrow \frac{-7+6}{2} \le -3+2 \Rightarrow \frac{-1}{2} \le -1 \Rightarrow -0.5 \le -1$. This is false.

D. $x=0$: $\frac{7(0)+6}{2} \le 3(0)+2 \Rightarrow \frac{6}{2} \le 2 \Rightarrow 3 \le 2$. This is false.

E. $x=1$: $\frac{7(1)+6}{2} \le 3(1)+2 \Rightarrow \frac{13}{2} \le 5 \Rightarrow 6.5 \le 5$. This is false.

F. $x=2$: $\frac{7(2)+6}{2} \le 3(2)+2 \Rightarrow \frac{14+6}{2} \le 6+2 \Rightarrow \frac{20}{2} \le 8 \Rightarrow 10 \le 8$. This is false.

G. $x=3$: $\frac{7(3)+6}{2} \le 3(3)+2 \Rightarrow \frac{21+6}{2} \le 9+2 \Rightarrow \frac{27}{2} \le 11 \Rightarrow 13.5 \le 11$. This is false.

Problem 2:

We need to solve the inequality $2x-3 > \frac{2x-5}{2}$.

Multiply both sides by 2:

$2(2x-3) > 2x-5$

$4x-6 > 2x-5$

Subtract $2x$ from both sides:

$2x-6 > -5$

Add 6 to both sides:

$2x > 1$

Divide both sides by 2:

$x > \frac{1}{2}$

3. Final Answer

Problem 1: A, B

Problem 2: B