A thermometer is considered accurate if its temperature reading, T degrees Fahrenheit, dif… — ACT

A thermometer is considered accurate if its temperature reading, $T$ degrees Fahrenheit, differs from the actual temperature by less than $1.5^\circ\text{F}$ . If the actual temperature is $72.0^\circ\text{F}$ , which of the following inequalities represents the range of reading temperatures, $T$ , that are NOT considered accurate?

A
$|T - 1.5| \ge 72.0$
B
$T - 72.0 \ge 1.5$
$|T - 72.0| \ge 1.5$ Cevap
D
$|T - 72.0| < 1.5$
E
$|T - 72.0| > 1.5$

Cevap

|T - 72.0| \ge 1.5

The difference between the temperature reading,

T

, and the actual temperature of

72.0^\circ\text{F}

is represented by

|T - 72.0|

. A thermometer is accurate when this difference is less than

1.5^\circ\text{F}

(

|T - 72.0| < 1.5

). Therefore, the thermometer is not accurate when the difference is greater than or equal to

1.5^\circ\text{F}

, which is written as

|T - 72.0| \ge 1.5

Adım Adım Çözüm

Represent the difference between the reading and the actual temperature.

|T - 72.0|

The difference between the reading temperature and the actual temperature of

72.0^\circ\text{F}

is given by the absolute value expression, representing the distance between the two temperatures on a thermometer.

Formulate the condition for an accurate reading.

|T - 72.0| < 1.5

An accurate reading differs from the actual temperature by less than

1.5^\circ\text{F}

Determine the complement condition for a reading that is NOT accurate.

|T - 72.0| \ge 1.5

To find the range of readings that are NOT accurate, we take the complement of the accurate condition. The opposite of 'less than

1.5

' is 'greater than or equal to

1.5

Anahtar Kavram

Absolute Value Inequalities in Real-World Contexts

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