Answer:
[tex] |x - 950| \le 250 [/tex]
Step-by-step explanation:
The minimum temperature is 700 deg C, so x, the temperature must be greater than or equal to 700.
[tex] x \ge 700 [/tex]
which can also be written as
[tex] 700 \le x [/tex]
The maximum temperature is 1200 deg C, so x, the temperature must be less than or equal to 1200.
[tex] x \le 1200 [/tex]
Put together the last two inequalities in a compound inequality to get
[tex] 700 \le x \le 1200 [/tex]
Now we need to change it into an absolute value inequality.
The average of the two temperatures is (700 + 900)/2 = 950. The difference between the two temperatures is 1200 - 700 = 500. Half of the difference is 250. The temperature, x, will vary from 250 less than 950 to 250 more than 250.
The absolute value equation is:
[tex] |x - 950| \le 250 [/tex]
