Question

1. reason abstractly compare and contrast the solutions $x < 2$ and $x \leq 2$.

Explanation:

Both solution sets include all real numbers less than 2. The key difference is that $x \leq 2$ also includes the value 2 itself, while $x < 2$ does not include 2. On a number line, $x < 2$ is represented with an open circle at 2 and a line extending left, and $x \leq 2$ uses a closed circle at 2 with a line extending left.

Answer:

• Similarity: Both include all real numbers $x$ where $x < 2$.
• Difference: $x \leq 2$ includes the value $x=2$, while $x < 2$ excludes $x=2$.