Question

Solve each equation. $$ \sqrt{3 x+1}=4 $$

   Solve each equation. 
$$
\sqrt{3 x+1}=4
$$

Impact Mathematics Algebra and More

Impact Mathematics Algebra and More

McGraw Hill 1st Edition

Chapter 7, Problem 2

Instant Answer

Solved by Expert Sriram Soundarrajan

07/03/2020

Step 1

We can do this by squaring both sides of the equation. This gives us: $$ (\sqrt{3x+1})^2 = 4^2 $$ Show more…

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Solve each equation. $$ \sqrt{3 x+1}=4 $$

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Key Concepts

Extraneous Solutions

Extraneous solutions are results that emerge from the process of squaring both sides of an equation but do not satisfy the original equation. After solving the squared equation, it is important to substitute potential solutions back into the original equation to verify that they are valid within the context of the problem.

Square Root Equations

Square root equations are equations that contain a square root expression with a variable inside it. They require special handling because the square root function is not defined for negative numbers, imposing natural domain restrictions on the variable. Understanding these restrictions is essential for finding valid solutions.

Squaring Both Sides

Squaring both sides of an equation is a common method used to eliminate square roots. By raising both sides of an equation to the power of two, the square root sign is removed, converting the equation into a polynomial equation that is often easier to solve. However, this technique requires caution as it can potentially introduce solutions that do not work in the original equation.

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