Question

On a road in the city of Madison, the maximum speed is 45 miles per hour and the minimum speed is 35 miles per hour. Let x represents the speed. You can write two inequalities to represent the speed restrictions. The inequalities and can be combined and can be written without using and.

a. Explain how compound inequalities can be use to describe the speed restrictions on roads.  

b. Include a compound inequality describing a possible age restriction for driving on roads. Describe what this represents. (Minimum driving age is 16 years, and most drivers stop renewing their licenses by age 100.)

Answer 1

a. 35 ≤ x ≤ 45

b. 16 ≤ x ≤ 100.

Explanation:

On a road in the city of Madison, the maximum speed is 45 miles per hour and minimum speed is 35 miles per hour.

If x represents the speed then

x ≥ 35

and x ≤ 45 are the inequalities to represent the speed restrictions.

(a) combined inequality will be 35 ≤ x ≤ 45

which shows the combined speed limits on the road.

(b) Let the driving age of a driver is x years.

So by the statement x ≥ 16 and x ≤ 100

When we combine these inequalities 16 ≤ x ≤ 100.

Answer 2

a. 35≤x≤45 where x represents speed

b. 16≤y≤100 where y represents age

Explanation:

a. Explain how compound inequalities can be use to describe the speed restrictions on roads.

x represents the speed, then

the maximum speed is 45 miles

x≤45

the minimum speed is 35 miles

x≥35

Both inequalities represent the speed restrictions

The compound inequality will be:

35≤x≤45

b. Include a compound inequality describing a possible age restriction for driving on roads. Describe what this represents. (Minimum driving age is 16 years, and most drivers stop renewing their licenses by age 100.)

Let y be the age

then

Minimum driving age is 16 years

y≥16

most drivers stop renewing their licenses by age 100.)

y≤100

The compound inequality will be:

16≤y≤100 ..