Solve 140=19[1+45*10^-3(T-200)]

$$140 = 19 [ 1 + 45 \times 10 ^ { - 3 } ( T - 200 ) ]$$

Solve for T

$$T = \frac{58400}{171} = 341\frac{89}{171} \approx 341.520467836$$

Steps for Solving Linear Equation

Divide both sides by 19.

$$\frac{140}{19}=1+45\times 10^{-3}\left(T-200\right)$$

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

$$\frac{140}{19}=1+45\times \frac{1}{1000}\left(T-200\right)$$

Multiply 45 and \frac{1}{1000} to get \frac{9}{200}.

$$\frac{140}{19}=1+\frac{9}{200}\left(T-200\right)$$

Use the distributive property to multiply \frac{9}{200} by T-200.

$$\frac{140}{19}=1+\frac{9}{200}T-9$$

Subtract 9 from 1 to get -8.

$$\frac{140}{19}=-8+\frac{9}{200}T$$

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

$$-8+\frac{9}{200}T=\frac{140}{19}$$

Add 8 to both sides.

$$\frac{9}{200}T=\frac{140}{19}+8$$

Add \frac{140}{19} and 8 to get \frac{292}{19}.

$$\frac{9}{200}T=\frac{292}{19}$$

Multiply both sides by \frac{200}{9}, the reciprocal of \frac{9}{200}.

$$T=\frac{292}{19}\times \frac{200}{9}$$

Multiply \frac{292}{19} and \frac{200}{9} to get \frac{58400}{171}.

$$T=\frac{58400}{171}$$