Question

traffic james is driving 75 miles per hour on an interstate highway. write and solve an inequality for n, the number of miles per hour james could reduce his speed to be within the legal range.
part a
select the inequality that represents the situation.
a)
b)
c)
d)
speed limit sign: 70 maximum, 40 minimum

Explanation:

Step1: Define the inequality

James's current speed is 75 mph. He reduces his speed by \( n \) mph, so his new speed is \( 75 - n \) mph. The legal speed range is between 40 mph (minimum) and 70 mph (maximum, from the speed limit sign). So the inequality representing his new speed being within the legal range is \( 40 \leq 75 - n \leq 70 \).

Step2: Solve the left - hand inequality (\( 40 \leq 75 - n \))

Subtract 75 from both sides: \( 40 - 75 \leq 75 - n - 75 \)
Simplify: \( - 35 \leq -n \)
Multiply both sides by - 1 (and reverse the inequality sign): \( 35\geq n \) or \( n\leq35 \)

Step3: Solve the right - hand inequality (\( 75 - n \leq 70 \))

Subtract 75 from both sides: \( 75 - n-75\leq70 - 75 \)
Simplify: \( -n\leq - 5 \)
Multiply both sides by - 1 (and reverse the inequality sign): \( n\geq5 \)

Answer:

The inequality is \( 40\leq75 - n\leq70 \), and the solution for \( n \) is \( 5\leq n\leq35 \)