To calibrate a temperature sensor, a technician uses the formula T_c = T_r - e, where T_c … — ACT

To calibrate a temperature sensor, a technician uses the formula $T_c = T_r - e$ , where $T_c$ is the calibrated temperature, $T_r$ is the raw sensor reading, and $e$ is the calibration error of the sensor. For a particular sensor, the calibration error is $-2.4^\circ\text{C}$ . If the calibrated temperature is measured to be $18.6^\circ\text{C}$ , which of the following equations can be solved to find the raw sensor reading, $T_r$ , in degrees Celsius?

A
$18.6 = T_r - 2.4$
$18.6 = T_r + 2.4$ Answer
C
$18.6 = 2.4 - T_r$
D
$18.6 = -2.4 - T_r$
E
$18.6 = \\frac{T_r}{-2.4}$

Answer

The equation

18.6 = T_r + 2.4

To find the correct equation, substitute the given values into the formula

T_c = T_r - e

. Substituting

T_c = 18.6

and

e = -2.4

yields

18.6 = T_r - (-2.4)

. Subtracting a negative number is equivalent to addition, which simplifies the equation to

18.6 = T_r + 2.4

Step-by-Step Solution

Identify the given variables and their values from the problem statement.

The calibrated temperature

T_c = 18.6

and the calibration error

e = -2.4

Knowing the values allows for direct substitution into the formula.

Substitute the identified values into the calibration formula

T_c = T_r - e

The equation becomes

18.6 = T_r - (-2.4)

This establishes the relationship between the raw reading

T_r

and the known values.

Simplify the subtraction of the negative number on the right side of the equation.

The equation simplifies to

18.6 = T_r + 2.4

Subtracting a negative number is mathematically equivalent to adding its positive counterpart.

Key Concept

Substituting signed values into algebraic expressions and simplifying one-step linear equations.

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