Question

Solve each equation or formula for the specified variable.

$\frac{a\left(b-2\right)}{c-3}=x$, for b.

Short answer

The required answer is $b=\frac{cx-3x+2a}{a}$.

Step-by-step solution

Step 1- Simplify the numerator of fraction on left side

Use distributive property $a\left(b+c\right)=ab+ac$ on left side of the equation.

$\frac{ab-2a}{c-3}=x$

Step 2- Multiply by c-3 on both sides of the equation

Perform multiplication of$c-3$ on both the sides of the equation.

$\begin{array}{c}c-3\left(\frac{ab-2a}{c-3}\right)=\left(c-3\right)\left(x\right)\\ ab-2a=cx-3x\end{array}$

– Isolate the variable b

Perform addition of 2a on both the sides of the equation.

$\begin{array}{c}ab-2a+2a=cx-3x+2a\\ ab=cx-3x+2a\end{array}$

Perform division of a on both the sides of the equation.

$\begin{array}{c}\frac{ab}{a}=\frac{cx-3x+2a}{a}\\ b=\frac{cx-3x+2a}{a}\end{array}$

Step 4- Make the conclusion

As the variable b is isolated so the value equivalent to it represents its value.