Solve y=7(3beta)-5/2-6(3B)

$$y = \frac { 7 ( 3 \beta ) - 5 } { 2 - 6 ( 3 B ) }$$

Solve for B

$$\left\{\begin{matrix}B=\frac{2y-21\beta +5}{18y}\text{, }&\beta \neq \frac{5}{21}\text{ and }y\neq 0\\B\neq \frac{1}{9}\text{, }&y=0\text{ and }\beta =\frac{5}{21}\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable B cannot be equal to \frac{1}{9} since division by zero is not defined. Multiply both sides of the equation by 2\left(-9B+1\right).

$$y\times 2\left(-9B+1\right)=7\times 3\beta -5$$

Use the distributive property to multiply y\times 2 by -9B+1.

$$-18yB+y\times 2=7\times 3\beta -5$$

Multiply 7 and 3 to get 21.

$$-18yB+y\times 2=21\beta -5$$

Subtract y\times 2 from both sides.

$$-18yB=21\beta -5-y\times 2$$

Multiply -1 and 2 to get -2.

$$-18yB=21\beta -5-2y$$

The equation is in standard form.

$$\left(-18y\right)B=-2y+21\beta -5$$

Divide both sides by -18y.

$$\frac{\left(-18y\right)B}{-18y}=\frac{-2y+21\beta -5}{-18y}$$

Dividing by -18y undoes the multiplication by -18y.

$$B=\frac{-2y+21\beta -5}{-18y}$$

Divide 21\beta -5-2y by -18y.

$$B=-\frac{-2y+21\beta -5}{18y}$$

Variable B cannot be equal to \frac{1}{9}.

$$B=-\frac{-2y+21\beta -5}{18y}\text{, }B\neq \frac{1}{9}$$

Solve for y

$$y=-\frac{5-21\beta }{2\left(1-9B\right)}$$

$$B\neq \frac{1}{9}$$