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steposvetlana [31]
2 years ago
14

In a certain town, the wind speed, x, in km/h on a certain day is described by two statements: If 2 times the wind speed is incr

eased by 2, the wind speed is still less than 46 km/h. Twice the wind speed minus 27 is greater than 11 km/h. Part A: Create a compound inequality to represent the wind speed range. (3 points) Part B: Can the wind speed in this town be 20 km/h? Justify your answer by solving the inequalities in Part A. (3 points) Part C: The average wind speed in another town is 23 km/h, but the actual wind speed is within 4 km/h of the average. Write and solve an inequality to find the range of wind speed in this town.
Mathematics
1 answer:
hodyreva [135]2 years ago
4 0
<span>1) if 2 times the wind speed is increased by 2, the wind speed is still less than 46 km/h.

=> 2x + 2 < 46

2) Twice the wind speed minus 27 is greater than 11 km/h.

=> 2x - 27 > 11

Part A: Create a compound inequality to represent the wind speed range. (3 points)


from 2x + 2 < 46

=> 2x < 44

=> x < 22

from 2x - 27 > 11

=> 2x > 11 + 27

=> 2x > 38

=> x > 19

The set of inequalities is

2x + 2 <46
2x - 27 > 11

The solution is x < 22 and x > 19, which is:

19 < x < 22 <----- answer

Part B: Can the wind speed in this town be 20 km/h? Justify your answer by solving the inequalities in Part A. (3 points)

Yes, the wind speed can be 20 km/h, because the solution of the inequality is the range (19,22).

Part C: The average wind speed in another town is 23 km/h, but the actual wind speed is within 4 km/h of the average. Write and solve an inequality to find the range of wind speed in this town.

x ≥ 23 - 4 => x ≥ 19

x ≤ 23 + 4=> x ≤ 27

=> 19 ≤ x ≤ 27

=> [19,27]
</span>
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