Solve 1.214=1+1.92*10^-3(T-273.15)

$$1.214 = 1 + 1.92 \times 10 ^ { - 3 } ( T - 273.15 )$$

Solve for T

$$T = \frac{46153}{120} = 384\frac{73}{120} \approx 384.608333333$$

Steps for Solving Linear Equation

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$1.214=1+1.92\times \frac{1}{1000}\left(T-273.15\right)$$

Multiply 1.92 and \frac{1}{1000} to get \frac{6}{3125}.

$$1.214=1+\frac{6}{3125}\left(T-273.15\right)$$

Use the distributive property to multiply \frac{6}{3125} by T-273.15.

$$1.214=1+\frac{6}{3125}T-\frac{16389}{31250}$$

Subtract \frac{16389}{31250} from 1 to get \frac{14861}{31250}.

$$1.214=\frac{14861}{31250}+\frac{6}{3125}T$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{14861}{31250}+\frac{6}{3125}T=1.214$$

Subtract \frac{14861}{31250} from both sides.

$$\frac{6}{3125}T=1.214-\frac{14861}{31250}$$

Subtract \frac{14861}{31250} from 1.214 to get \frac{46153}{62500}.

$$\frac{6}{3125}T=\frac{46153}{62500}$$

Multiply both sides by \frac{3125}{6}, the reciprocal of \frac{6}{3125}.

$$T=\frac{46153}{62500}\times \frac{3125}{6}$$

Multiply \frac{46153}{62500} and \frac{3125}{6} to get \frac{46153}{120}.

$$T=\frac{46153}{120}$$