World Records in the 1500-m Run. The formula R = -0.075t + 3.85 can be used to predict the world record in the 1500-m run t years after 1930. Determine (in terms of an inequality) those years for which the world record will be less than 3.5 min.
you just need t where
-0.075t + 3.85 < 3.5
0.075t > 0.35
t > 4.67
So, any year after 1935
To determine the years for which the world record in the 1500-m run will be less than 3.5 minutes, we need to solve the inequality R < 3.5, where R represents the predicted world record.
Given the formula R = -0.075t + 3.85, we can substitute the value for R into the inequality:
-0.075t + 3.85 < 3.5
Next, we can simplify the inequality:
-0.075t < 3.5 - 3.85
-0.075t < -0.35
To isolate t, divide both sides of the inequality by -0.075, remembering that dividing both sides by a negative number reverses the direction of the inequality:
t > (-0.35) / (-0.075)
t > 4.67
Since t represents the number of years after 1930, we can conclude that the world record will be less than 3.5 minutes for all years after 1930 when t is greater than 4.67.
Inequality: t > 4.67