Chapter 1: Q61. (page 25)

Solve each equation or formula for the specified variable.
$\frac{a (b - 2)}{c - 3} = x$ , for b.

Short Answer

Expert verified

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

Step by step solution

Step 1- Simplify the numerator of fraction on left side

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

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

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

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

$\begin{matrix} c - 3 (\frac{a b - 2 a}{c - 3}) = (c - 3) (x) \\ a b - 2 a = c x - 3 x \end{matrix}$

– Isolate the variable b

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

$\begin{matrix} a b - 2 a + 2 a = c x - 3 x + 2 a \\ a b = c x - 3 x + 2 a \end{matrix}$

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

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

Step 4- Make the conclusion

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

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Solve each equation or formula for the specified variable.
$\frac{a (b - 2)}{c - 3} = x$ , for b.

Short Answer

Step by step solution

Step 1- Simplify the numerator of fraction on left side

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

– Isolate the variable b

Step 4- Make the conclusion

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Solve each equation or formula for the specified variable.ab-2c-3=x, for b.

Short Answer

Step by step solution

Step 1- Simplify the numerator of fraction on left side

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

– Isolate the variable b

Step 4- Make the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Mechanics Maths

Theoretical and Mathematical Physics

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve each equation or formula for the specified variable.
$\frac{a (b - 2)}{c - 3} = x$ , for b.