A meteorologist announces that yesterday’s high temperature was within 4° Celsius of 18° Celsius all across the country. Write an inequality that involves an absolute value to represent yesterday’s high temperature. Solve the inequality and explain the meaning of the solution.
I'm really struggling with this question! I've started with something like, "|x-18|=4" but I don't know where to go from there, if that's even the correct beginning:/ And what's the meaning of the solution(!)? Any help would be appreciated, thank you.
Wouldn't the temperature be between 14 and 22 ?
so
14 ≤ T ≤ 22
you were on the right track with |T - 18|
but you should have said:
|T - 18| ≤ 4
then T-18 ≤ 4 and -T + 18 ≤ 4
T ≤ 22 and -T ≤ -14 ----> T ≥ 14
the connective "and" allows me to write it as
14 ≤ T ≤ 22 , as above
Thank you, Reiny!:) that really helped!
You're on the right track! Starting with the equation "|x - 18| = 4" is a good beginning. To solve this equation, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
1. Case when x - 18 is positive:
In this case, the equation becomes x - 18 = 4. To solve for x, we can add 18 to both sides of the equation:
x - 18 + 18 = 4 + 18
x = 22
2. Case when x - 18 is negative:
In this case, the equation becomes -(x - 18) = 4. When you distribute the negative sign, it becomes -x + 18 = 4. To solve for x, we can subtract 18 from both sides of the equation:
-x + 18 - 18 = 4 - 18
-x = -14
To solve for x, we need to multiply both sides of the equation by -1 to isolate x:
(-1)(-x) = (-1)(-14)
x = 14
So the solutions to the equation "|x - 18| = 4" are x = 22 and x = 14.
Now, let's interpret the meaning of these solutions. The meteorologist stated that yesterday's high temperature was within 4° Celsius of 18° Celsius all across the country. The equation |x - 18| = 4 represents this statement.
The solution x = 22 means that there was a location where the high temperature was 22° Celsius, which is 4 degrees higher than 18° Celsius. The solution x = 14 means that there was a location where the high temperature was 14° Celsius, which is 4 degrees lower than 18° Celsius.
Therefore, the statement by the meteorologist can be understood as: Yesterday's high temperature across the country ranged from 14° Celsius to 22° Celsius, with all temperatures falling no more than 4 degrees away from 18° Celsius in either direction.
A meteorologist announces that yesterday’s high temperature was within 4° Celsius of 18° Celsius all across the country. Write an inequality that involves an absolute value to represent yesterday’s high temperature. Solve the inequality and explain the meaning of the solution.
I'm really struggling with this question! I've started with something like, "|x-18|=4" but I don't know where to go from there, if that's even the correct beginning:/ And what's the meaning of the solution(!)? Any help would be appreciated, thank you.