The problem consists of two inequalities. First, given $x+3 \ge 7$, prove that $x \ge 4$. Second, given $y-3 > 2$, prove that $y > 5$.

1. Problem Description

The problem consists of two inequalities.

First, given $x+3 \ge 7$, prove that $x \ge 4$.

Second, given $y-3 > 2$, prove that $y > 5$.

2. Solution Steps

Part 1:

We are given the inequality $x+3 \ge 7$.

To isolate $x$, we subtract 3 from both sides of the inequality:

$x+3-3 \ge 7-3$

$x \ge 4$

Thus, we have shown that if $x+3 \ge 7$, then $x \ge 4$.

Part 2:

We are given the inequality $y-3 > 2$.

To isolate $y$, we add 3 to both sides of the inequality:

$y-3+3 > 2+3$

$y > 5$

Thus, we have shown that if $y-3 > 2$, then $y > 5$.

3. Final Answer

Part 1: $x \ge 4$

Part 2: $y > 5$