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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.

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


Learn more about this topic:

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Solving Equations Using the Addition Principle

from Algebra I: High School

Chapter 8 / Lesson 11
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