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Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 1 - Equations and InequalitiesProblema 47
Capitolo 2, Problema 47

In Exercises 45–47, solve each formula for the specified variable. T = (A-P)/Pr for P

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Start with the given formula: T=A-PPr. The goal is to solve for P.
Multiply both sides of the equation by Pr to eliminate the denominator: TPr=A-P.
Rearrange the equation to isolate terms involving P on one side. Add P to both sides: TPr+P=A.
Factor out P from the left-hand side: P(Tr+1)=A.
Divide both sides of the equation by Tr+1 to solve for P: P=ATr+1.

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Algebraic Manipulation

Algebraic manipulation involves rearranging equations to isolate a specific variable. This process includes operations such as addition, subtraction, multiplication, and division applied to both sides of the equation to maintain equality. Understanding how to manipulate equations is essential for solving for a variable, as it allows one to express the variable in terms of others.
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Introduction to Algebraic Expressions

Formulas and Variables

A formula is a mathematical relationship expressed in symbols, often involving multiple variables. In the given equation, T, A, P, and r are variables that represent different quantities. Recognizing the roles of these variables and how they interact within the formula is crucial for solving for the desired variable, in this case, P.
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Equations with Two Variables

Isolating the Variable

Isolating the variable means rearranging the equation so that the variable of interest stands alone on one side. This often requires inverse operations to eliminate other variables from that side. In the context of the given formula, isolating P involves strategically applying algebraic operations to express P in terms of T, A, and r.
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Equations with Two Variables
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