Solve 121=frac{{b}_{1}left(1/243-1right)}{-2/3}

$$121 = \frac{ { b }_{ 1 } \left( \frac{ 1 }{ 243 } -1 \right) }{ - \frac{ 2 }{ 3 } }$$

Solve for b_1

$$b_{1}=81$$

Steps for Solving Linear Equation

Multiply both sides by -\frac{2}{3}.

$$121\left(-\frac{2}{3}\right)=b_{1}\left(\frac{1}{243}-1\right)$$

Express 121\left(-\frac{2}{3}\right) as a single fraction.

$$\frac{121\left(-2\right)}{3}=b_{1}\left(\frac{1}{243}-1\right)$$

Multiply 121 and -2 to get -242.

$$\frac{-242}{3}=b_{1}\left(\frac{1}{243}-1\right)$$

Fraction \frac{-242}{3} can be rewritten as -\frac{242}{3} by extracting the negative sign.

$$-\frac{242}{3}=b_{1}\left(\frac{1}{243}-1\right)$$

Convert 1 to fraction \frac{243}{243}.

$$-\frac{242}{3}=b_{1}\left(\frac{1}{243}-\frac{243}{243}\right)$$

Since \frac{1}{243} and \frac{243}{243} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{242}{3}=b_{1}\times \frac{1-243}{243}$$

Subtract 243 from 1 to get -242.

$$-\frac{242}{3}=b_{1}\left(-\frac{242}{243}\right)$$

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

$$b_{1}\left(-\frac{242}{243}\right)=-\frac{242}{3}$$

Multiply both sides by -\frac{243}{242}, the reciprocal of -\frac{242}{243}.

$$b_{1}=-\frac{242}{3}\left(-\frac{243}{242}\right)$$

Multiply -\frac{242}{3} times -\frac{243}{242} by multiplying numerator times numerator and denominator times denominator.

$$b_{1}=\frac{-242\left(-243\right)}{3\times 242}$$

Do the multiplications in the fraction \frac{-242\left(-243\right)}{3\times 242}.

$$b_{1}=\frac{58806}{726}$$

Divide 58806 by 726 to get 81.

$$b_{1}=81$$