Solve 140=19[1+4.5*10^-3(T-20.0)]

$$140 = 19 [ 1 + 4.5 \times 10 ^ { - 3 } ( T - 20.0 ) ]$$

Solve for T

$$T = \frac{245420}{171} = 1435\frac{35}{171} \approx 1435.204678363$$

Steps for Solving Linear Equation

Divide both sides by 19.

$$\frac{140}{19}=1+4.5\times 10^{-3}\left(T-20\right)$$

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

$$\frac{140}{19}=1+4.5\times \frac{1}{1000}\left(T-20\right)$$

Multiply 4.5 and \frac{1}{1000} to get \frac{9}{2000}.

$$\frac{140}{19}=1+\frac{9}{2000}\left(T-20\right)$$

Use the distributive property to multiply \frac{9}{2000} by T-20.

$$\frac{140}{19}=1+\frac{9}{2000}T-\frac{9}{100}$$

Subtract \frac{9}{100} from 1 to get \frac{91}{100}.

$$\frac{140}{19}=\frac{91}{100}+\frac{9}{2000}T$$

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

$$\frac{91}{100}+\frac{9}{2000}T=\frac{140}{19}$$

Subtract \frac{91}{100} from both sides.

$$\frac{9}{2000}T=\frac{140}{19}-\frac{91}{100}$$

Subtract \frac{91}{100} from \frac{140}{19} to get \frac{12271}{1900}.

$$\frac{9}{2000}T=\frac{12271}{1900}$$

Multiply both sides by \frac{2000}{9}, the reciprocal of \frac{9}{2000}.

$$T=\frac{12271}{1900}\times \frac{2000}{9}$$

Multiply \frac{12271}{1900} and \frac{2000}{9} to get \frac{245420}{171}.

$$T=\frac{245420}{171}$$