Ch. 1 - Equations and Inequalities

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 1 - Equations and Inequalities

Problem 5

Chapter 2, Problem 5

Solve each equation. A= 24f / B(p+1), for f (approximate annual interest rate)

Verified step by step guidance

Start with the given equation: \(A = \frac{24f}{B(p+1)}\).

To isolate \(f\), multiply both sides of the equation by the denominator \(B(p+1)\) to eliminate the fraction: \(A \times B(p+1) = 24f\).

Rewrite the equation as \(A B (p+1) = 24f\) to clearly show the product on the left side.

Divide both sides of the equation by 24 to solve for \(f\): \(f = \frac{A B (p+1)}{24}\).

Now, \(f\) is expressed in terms of \(A\), \(B\), and \(p\), which completes the isolation of \(f\).

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Key Concepts

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

Solving for a Variable in an Equation

This involves isolating the desired variable on one side of the equation by performing algebraic operations such as multiplication, division, addition, or subtraction. The goal is to rewrite the equation so that the variable is expressed explicitly in terms of the other variables and constants.

Understanding Variables and Constants

Variables represent unknown or changeable quantities, while constants are fixed values. Recognizing which symbols are variables and which are constants helps in manipulating the equation correctly and understanding the relationships between different quantities.

Fractional Equations and Cross-Multiplication

When variables appear in denominators or as part of fractions, cross-multiplication is a useful technique to eliminate fractions and simplify the equation. This involves multiplying both sides of the equation by the denominators to clear fractions and make solving for the variable easier.

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