Question

active practice:
the speed limit is 35 mph. write an inequality showing the speed you can legally drive in this zone.
\\( n > 35 \\)
\\( n \leq 35 \\)
\\( n = 35 \\)
\\( n < 35 \\)
\\( n \geq 35 \\)

Explanation:

Step1: Understand the problem

The speed limit is 35 mph, which means the legal speed \( s \) (let's use \( s \) instead of \( b \) for clarity, but the variable name doesn't change the logic) can be at most 35 mph. So the speed can be equal to 35 or less than 35.

Step2: Analyze the inequalities

• \( s>35 \): Speed greater than 35, which is over the limit, illegal.
• \( s\leq35 \): Speed less than or equal to 35, which is legal (including exactly 35).
• \( s = 35 \): Only exactly 35, but legal speed can also be less, so this is too restrictive.
• \( s<35 \): Speed less than 35, but 35 itself is also legal, so this misses the equal case.
• \( s\geq35 \): Speed greater than or equal to 35, which includes over the limit, illegal.

Answer:

\( b \leq 35 \) (the option with \( b \leq 35 \))