/*! 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 49 \(t=27-\frac{1}{4}(w-l),\) for \... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 49

\(t=27-\frac{1}{4}(w-l),\) for \(l\)

Short Answer

Expert verified
l = 4t - 108 + w

Step by step solution

01

Isolate the term involving l

Start by isolating the term that contains the variable l. You have the equation: \[ t = 27 - \frac{1}{4}(w - l) \]Subtract 27 from both sides to isolate the term with l: \[ t - 27 = -\frac{1}{4}(w - l) \]
02

Eliminate the Fraction

To eliminate the fraction, multiply both sides of the equation by -4: \[ -4(t - 27) = w - l \]This simplifies to: \[ -4t + 108 = w - l \]
03

Isolate the variable l

Finally, isolate l by moving the other terms to the opposite side of the equation. Add l and then subtract -4t and 108 from both sides: \[ -4t + 108 - w = -l \]Multiply by -1 to solve for l: \[ l = 4t - 108 + w \]

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.

Variable Isolation
To solve equations, it's essential to isolate the variable you need to find. This means we want to get the variable on one side by itself. In the given problem, we start by isolating the term that includes the variable we're solving for, which is 'l'. To do this, we move terms without 'l' to the other side of the equation. For example:
The initial equation: \( t = 27 - \frac{1}{4}(w - l) \)
We subtract 27 from both sides to aim for isolating 'l': \( t - 27 = -\frac{1}{4}(w - l) \)
Remember, whatever operation you do to one side, you must do to the other! This ensures the equation stays balanced.
Eliminating Fractions
Fractions can make solving equations trickier, but you can eliminate them by multiplying both sides of the equation by the denominator. In our case, the fraction is \( \frac{1}{4} \). We want to eliminate it by multiplying both sides by 4, which results in:
The first adjustment: \( t - 27 = -\frac{1}{4}(w - l) \)
Multiply both sides by -4: \( -4(t - 27) = w - l \)
This simplifies to: \( -4t + 108 = w - l \)
By doing this step, you can manage the equation more easily and proceed to isolate the desired variable without handling fractions.
Linear Equations
A linear equation is an equation where the highest power of the variable is one. Solving linear equations generally involves steps like isolating variables and simplifying terms.
In our example, after eliminating fractions, we're left with: \( -4t + 108 = w - l \)
Finally, we'll isolate 'l' by bringing other terms to the other side:
Add 'l' to both sides and subtract '-4t' and '108': \( -4t + 108 - w = -l \)
To solve for 'l', multiply by -1: \( l = 4t - 108 + w \)
Understanding how to manage linear equations is a fundamental skill in algebra. These methods help one dismantle problems piece by piece for an eventual solution.

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

To prepare for Section \(2.6,\) review inequalities. Write a second inequality with the same meaning. $$5>y$$

Solve $$ x

To prepare for Section \(2.6,\) review inequalities. Write a second inequality with the same meaning. $$x \geq-4$$

Use an inequality and the five-step process to solve each problem. In order to qualify for a batting title, a major-league baseball player must average at least 3.1 plate appearances per game. For the first nine games of the season, a player had \(5,1,4,2,3,4,4,3,\) and 2 plate appearances. How many plate appearances must the player have in the tenth game in order to average at least 3.1 per game?

After 9 quizzes, Blythe's average is 84. Is it possible for Blythe to improve her average by two points with the next quiz? Why or why not?
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Decision 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.