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

1:22 minutes

Problem 67c

Textbook Question

Solve each equation. See Examples 4–6. ∛(4x+3)=∛(2x-1)

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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 context of the equation ∛(4x+3)=∛(2x-1), understanding cube roots is essential for simplifying both sides of the equation. This concept allows us to eliminate the cube roots by cubing both sides, leading to a polynomial equation that can be solved for 'x'.

Equating Expressions

When two expressions are equal, we can set them equal to each other to find the variable's value. In this case, after removing the cube roots, we will have the equation 4x + 3 = 2x - 1. This principle of equating expressions is fundamental in algebra, as it allows us to isolate the variable and solve for it systematically.

Solving Linear Equations

Solving linear equations involves isolating the variable on one side of the equation. After equating the expressions from the previous step, we will rearrange the equation to solve for 'x'. This process typically includes combining like terms and using inverse operations, which are key skills in algebra that lead to finding the solution.