Table of contents

0. Review of Algebra4h 18m
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 22m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Linear Equations

College Algebra

1. Equations & Inequalities

Linear Equations

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0:53 minutes

Problem 71

Textbook Question

Solve each equation. See Examples 4–6. ∜(x-15)=2

Verified step by step guidance

Start by understanding that the equation involves a fourth root: \( \sqrt[4]{x-15} = 2 \).

To eliminate the fourth root, raise both sides of the equation to the power of 4: \( (\sqrt[4]{x-15})^4 = 2^4 \).

Simplify both sides: \( x - 15 = 16 \).

Solve for \( x \) by adding 15 to both sides: \( x = 16 + 15 \).

Verify your solution by substituting \( x \) back into the original equation to ensure both sides are equal.

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Key Concepts

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

Radical Expressions

Radical expressions involve roots, such as square roots or fourth roots, which are denoted by the radical symbol (√). In the given equation, ∜(x-15) represents the fourth root of (x-15). Understanding how to manipulate and simplify these expressions is crucial for solving equations that involve them.

Isolating the Variable

Isolating the variable is a fundamental algebraic technique used to solve equations. This involves rearranging the equation to get the variable on one side and the constants on the other. In the context of the given equation, you would first eliminate the radical by raising both sides to the fourth power, allowing you to isolate x.

Exponents and Their Properties

Exponents represent repeated multiplication and have specific properties that govern their manipulation. For instance, raising a number to a power and then taking the root can be expressed as an exponent operation. In this case, understanding how to apply the property of exponents when raising both sides of the equation to the fourth power is essential for finding the solution.