The problem has two parts. Part 1: Given that $x+3 \ge 7$, show that $x \ge 4$. Part 2: Given that $y-3 > 2$, show that $y > 5$.

1. Problem Description

The problem has two parts.

Part 1: Given that $x+3 \ge 7$, show that $x \ge 4$.

Part 2: Given that $y-3 > 2$, show that $y > 5$.

2. Solution Steps

Part 1:

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

Subtract 3 from both sides of the inequality:

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

$x \ge 4$

Part 2:

We are given $y-3 > 2$.

Add 3 to both sides of the inequality:

$y - 3 + 3 > 2 + 3$

$y > 5$

3. Final Answer

Part 1: $x \ge 4$

Part 2: $y > 5$