Express each statement using an inequality involving absolute value.Do not solve.
1.The majority of grades in Sean's English class are within 4 points of 85.
2.AA thermometer is guaranteed to give a temperature no more than 1.2F from the actual temperature. If the thermometer reads 28F, what is the range for the actual temperature?
How would I solve these questions? Thanks
| g-85 | </= 4
do the temp one the same way
Could you explain more on why you put
| g-85 | </= 4 ? Thanks
In problems like this always say "what if"
If a grade were 87
|87-85| = |2| = 2 within 4 of 85
if it were 83
|83 -85| = |-2| = 2 within 4 of 85
but
if it were 80
|80-85| = |-5| = 5 not within 4
Would the second one be |28 - t|</= 1.2?
To express each statement using an inequality involving absolute value, we need to understand how absolute value works. The absolute value of a number is the distance from that number to zero on the number line. It is always a non-negative value.
1. The majority of grades in Sean's English class are within 4 points of 85.
Let's assume x represents the grades in Sean's English class. To express the statement using an inequality involving absolute value, we can say:
| x - 85 | < 4
This inequality states that the absolute value of the difference between the grade (x) and 85 is less than 4. To solve this inequality, we would need to find the values of x that satisfy this condition.
2. A thermometer is guaranteed to give a temperature no more than 1.2F from the actual temperature. If the thermometer reads 28F, what is the range for the actual temperature?
Let's assume t represents the actual temperature. To express the statement using an inequality involving absolute value, we can say:
| t - 28 | ≤ 1.2
This inequality states that the absolute value of the difference between the actual temperature and 28 is less than or equal to 1.2. To find the range for the actual temperature, we would need to solve this inequality for t.
By rearranging the inequality, we can express it in two separate inequalities:
t - 28 ≤ 1.2 (the actual temperature is 1.2F higher than the thermometer reading)
t - 28 ≥ -1.2 (the actual temperature is 1.2F lower than the thermometer reading)
To find the range, we solve both inequalities separately.