Solve each radical equation. Check your solution. √(3 x+1)=√(5 x-8)

Name: Problem 19, Chapter 10: Algebra 1 Common Core
Uploaded: 2020-04-03T01:47:29-08:00
Duration: 2 min 19 s
Channel: Julie Silva
Description: Solve each radical equation. Check your solution. √(3 x+1)=√(5 x-8)

step 1 We're being asked to solve the given radical equation. Well, because both radicals are isolated,

Solve each radical equation. Check your solution. √(3...

Key Concepts

Radical Equations

Radical equations involve variables under a radical sign, such as a square root. They require procedures to isolate the radical term and then eliminate the radical by raising both sides of the equation to an appropriate power. The process must be handled with care to ensure that all operations are valid within the real number system.

Domain Restrictions

When solving equations that include radicals, it is essential to establish the domain of the variables. For square roots, the expression inside the radical must be non-negative, which defines the set of possible values that the variable can take. This consideration prevents potential errors when solving the equation.

Squaring Both Sides

A common method used to remove a square root from an equation is squaring both sides. This step transforms the equation into an algebraic equation without radicals. However, squaring can introduce solutions that are not valid for the original equation, making it crucial to handle this step with care.

Extraneous Solutions

Extraneous solutions are results that appear as valid answers after algebraic manipulation, such as squaring, but do not satisfy the original equation. Identifying and removing these incorrect solutions is a critical part of solving radical equations.

Checking Solutions

After solving a radical equation, it is important to substitute the solutions back into the original equation to verify their validity. This process confirms that the solutions do not violate any domain restrictions or arise from the algebraic steps, such as squaring, that may introduce extraneous answers.

Transcript

Please give Ace some feedback