Table of contents

0. Review of Algebra4h 16m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 19m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Linear Equations

College Algebra

1. Equations & Inequalities

Linear Equations

1:27 minutes

Problem 68b

Textbook Question

Solve each equation. See Examples 4–6. ∛2x=∛(5x+2)

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Cube Roots

The cube root of a number 'a' is a value 'b' such that b³ = a. In the equation ∛2x = ∛(5x + 2), understanding how to manipulate cube roots is essential. This involves recognizing that if two cube roots are equal, then their radicands (the expressions inside the cube roots) must also be equal, leading to the equation 2x = 5x + 2.

Algebraic Manipulation

Algebraic manipulation involves rearranging and simplifying equations to isolate variables. In solving the equation derived from the cube roots, you will need to combine like terms and isolate 'x' to find its value. This skill is fundamental in algebra, allowing for the solution of various types of equations.

Checking Solutions

After finding a potential solution for 'x', it is crucial to check the solution by substituting it back into the original equation. This step ensures that the solution is valid and satisfies the equation. In this case, substituting the value of 'x' back into the original cube root equation will confirm whether the left-hand side equals the right-hand side.