# Solve: square root 3 b + square root 2 = square root 7 b - 10. a) none. b) 3. c) -3. d) -4.

## Question:

Solve: {eq}\sqrt 3 b + \sqrt 2 = \sqrt 7 b - 10 {/eq}.

a) none.

b) 3.

c) -3.

d) -4.

## Solving an Equation

Solving an equation of one variable means finding the value of the unknown variable. In this question, we have to find the value of **b**. This is done by bringing together the like terms, taking out the common terms and then simplifying.

## Answer and Explanation:

We can solve the equation, i.e. find the value of **b** as follows.

$$\begin{align} &\sqrt 3 b + \sqrt 2 = \sqrt 7 b - 10\\ &\sqrt 2+10=\sqrt 7 b-\sqrt 3b \\ &\sqrt 2+10=b(\sqrt 7-\sqrt 3)\\ &\frac{\sqrt 2+10}{\sqrt 7-\sqrt 3}=b\\ \therefore \,&b=12.49 \end{align} $$

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Solving Equations Using the Addition Principle

from Algebra I: High School

Chapter 8 / Lesson 11
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