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Zorluk: ZorBasic Algebraic Expressions and One-Step Equations

To calibrate a temperature sensor, a technician uses the formula Tc=Tr−eT_c = T_r - e, where TcT_c is the calibrated temperature, TrT_r is the raw sensor reading, and ee is the calibration error of the sensor. For a particular sensor, the calibration error is −2.4∘C-2.4^\circ\text{C}. If the calibrated temperature is measured to be 18.6∘C18.6^\circ\text{C}, which of the following equations can be solved to find the raw sensor reading, TrT_r, in degrees Celsius?

  1. A
    18.6=Tr−2.418.6 = T_r - 2.4
  2. 18.6=Tr+2.418.6 = T_r + 2.4Cevap
  3. C
    18.6=2.4−Tr18.6 = 2.4 - T_r
  4. D
    18.6=−2.4−Tr18.6 = -2.4 - T_r
  5. E
    18.6=fracTr−2.418.6 = \\frac{T_r}{-2.4}

Cevap

The equation 18.6=Tr+2.418.6 = T_r + 2.4
To find the correct equation, substitute the given values into the formula Tc=Tr−eT_c = T_r - e. Substituting Tc=18.6T_c = 18.6 and e=−2.4e = -2.4 yields 18.6=Tr−(−2.4)18.6 = T_r - (-2.4). Subtracting a negative number is equivalent to addition, which simplifies the equation to 18.6=Tr+2.418.6 = T_r + 2.4.

Adım Adım Çözüm

1
Identify the given variables and their values from the problem statement.
The calibrated temperature Tc=18.6T_c = 18.6 and the calibration error e=−2.4e = -2.4.
Knowing the values allows for direct substitution into the formula.
2
Substitute the identified values into the calibration formula Tc=Tr−eT_c = T_r - e.
The equation becomes 18.6=Tr−(−2.4)18.6 = T_r - (-2.4).
This establishes the relationship between the raw reading TrT_r and the known values.
3
Simplify the subtraction of the negative number on the right side of the equation.
The equation simplifies to 18.6=Tr+2.418.6 = T_r + 2.4.
Subtracting a negative number is mathematically equivalent to adding its positive counterpart.

Anahtar Kavram

Substituting signed values into algebraic expressions and simplifying one-step linear equations.
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Basic Algebraic Expressions and One-Step Equations

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