/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 92 Solve each formula for the indic... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 92

Solve each formula for the indicated variable. $$ a+(n-1) d=l \text { for } n $$

Short Answer

Expert verified
\( n = \frac{l - a}{d} + 1 \)

Step by step solution

01

Isolate the Term with Variable

Start by isolating the term that contains the variable you want to solve for, which is \(n\). The current equation is \(a + (n-1)d = l\). To isolate \((n-1)d\), subtract \(a\) from both sides: \((n-1)d = l - a\).
02

Divide to Solve for the Parenthesis

Next, you need to isolate \(n-1\) by removing \(d\). Divide both sides of the equation by \(d\): \(n-1 = \frac{l - a}{d}\).
03

Solve for the Variable

Finally, solve for \(n\) by adding 1 to both sides of the equation: \(n = \frac{l - a}{d} + 1\). This gives you \(n\) in terms of \(a\), \(d\), and \(l\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Solving for a Variable
When faced with algebraic expressions, one of the common tasks in math is to solve for a particular variable. Consider the equation given in the problem:
  • Start with identifying which variable you need to solve for: in this case, it's \(n\).
  • Recognize that the term containing the variable must be isolated on one side of the equation.
For example, if you have an equation like \(a + (n-1)d = l\), you should first focus on isolating \((n-1)d\) by subtracting \(a\) from both sides. This simplifies the process and sets the stage to finally solve for \(n\). Remember that you aim to get the variable alone on one side. Keep operations consistent and follow through each step methodically.
Equation Solving
Equation solving involves systematically working through an equation to identify the solution for the desired variable. In the equation \(a + (n-1)d = l\), you are performing several strategic manipulations:
  • Isolation and Simplification: Begin by isolating the term that contains the variable of interest. Subtract \(a\) from both sides to move non-variable terms away. This results in \((n-1)d = l - a\).
  • Use of Division: To reduce the equation further, divide by \(d\) to isolate \(n-1\). When you perform division, ensure correctness by dividing the entire expression on one side of the equation by the divisor.
This careful approach ensures that each step logically follows from the last, leading to a correct and simplified form of the equation.
Intermediate Algebra Concepts
Understanding how to manipulate and solve equations involves several key concepts in algebra. In intermediate algebra, you鈥檒l often:
  • Factor and Reorganize: Equations may sometimes require you to factorize expressions or reorganize terms for simpler manipulation.
  • Arithmetic Operations: These include adding, subtracting, multiplying, or dividing terms to isolate and solve for variables.
  • Expression Manipulation: Just like moving \((n-1)d\) to one side in the problem, you'll reorder and simplify various components of an equation.
Typically, you'll also deal with fractions, exponents, and other algebraic structures in intermediate algebra. The key is to apply these operations systematically and consistently to solve equations effectively. Understanding these building blocks will provide greater insight into solving more complex algebraic problems in the future.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Write an equation for a linear function whose graph has the given characteristics. Passes through \((1,7)\) and \((-2,1)\)

For each of the following functions, first sketch the graph of its associated function, \(f(x)=x^{2}, f(x)=x^{3},\) or \(f(x)=|x|\) Then draw the graph of function g using trans/ations and/or a reflection. See Examples 7 and 8 . $$ g(x)=-x^{2} $$

Real Estate. \(\quad\) A house purchased for \(\$ 275,000\) is expected to be worth \(\$ 282,000\) in 2 years. Find the straight-line appreciation equation for the house if it continues to appreciate at the same rate. What will the house be worth in 10 years?

Solve each formula for the indicated variable. $$ s=\frac{1}{2} g t^{2}+v t \text { for } g $$

Graph each equation. \(y=\frac{x-3}{|x-3|}\)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.