Final answer:
To find the range for the number of key presses, we solve the compound inequality 620 < 1200 - 0.05x < 680 separately for each part and combine the results to get 10400 < x < 11600.
Step-by-step explanation:
The given compound inequality is 620 < 1200 - 0.05x < 680. To find the range for the number of key presses (x), we solve the inequality in two parts:
- 1200 - 0.05x > 620
- 1200 - 0.05x < 680
For the first part:
1200 - 0.05x > 620
-0.05x > 620 - 1200
-0.05x > -580
x < 580 / 0.05
x < 11600 (after dividing by -0.05, change the inequality direction)
For the second part:
1200 - 0.05x < 680
-0.05x < 680 - 1200
-0.05x < -520
x > 520 / 0.05
x > 10400 (after dividing by -0.05, change the inequality direction)
Combining the two parts, we get 10400 < x < 11600. This is the range for the number of key presses, rounded to the nearest whole number.