step 1 When it comes to cube roots, you have a little bit more flexibility than you did square roots. H

Question

Solve. $\sqrt[3]{6 x+4}=4$

Name: Problem 305, Chapter 8: Intermediate Algebra
Uploaded: 2022-09-25T02:50:03-08:00
Channel: Alison Rodriguez
Description: Solve. √(6 x+4)=4

   Solve.
$\sqrt[3]{6 x+4}=4$

Intermediate Algebra

Lynn Marecek 2nd Edition

Chapter 8, Problem 305

Instant Answer

Solved by Expert Alison Rodriguez

09/25/2022

Step 1

To do this, we cube both sides of the equation. This gives us: $$(\sqrt[3]{6 x+4})^3 = 4^3$$ Show more…

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Solve. $\sqrt[3]{6 x+4}=4$

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Key Concepts

Cube Roots

The cube root of a number is the value that, when raised to the third power, reproduces the original number. This concept is crucial for understanding equations where the cube root function is applied, as it allows one to reverse the operation by cubing both sides of the equation.

Inverse Operations

Inverse operations are fundamental in solving equations. When a function is applied to a variable, applying its inverse function can undo the effect. In the case of the cube root, cubing both sides of the equation effectively cancels the cube root, making it easier to isolate the variable.

Linear Equation Solving

After applying the inverse operation to eliminate the cube root, the problem often reduces to a linear equation. Solving a linear equation involves simplifying the equation and isolating the variable using basic arithmetic operations.

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