Textbook Question
Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. (3x+1)/3 - 13/2 = (1-x)/4
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 2, Problem 27
The length of the rectangular tennis court at Wimbledon is 6 feet longer than twice the width. If the court's perimeter is 228 feet, what are the court's dimensions?
Verified step by step guidance1
Define variables for the dimensions of the tennis court: let the width be \(w\) feet, and the length be \(l\) feet.
Express the length in terms of the width using the given relationship: \(l = 2w + 6\).
Recall the formula for the perimeter of a rectangle: \(P = 2l + 2w\). Substitute the given perimeter value: \(228 = 2l + 2w\).
Substitute the expression for \(l\) from step 2 into the perimeter equation: \(228 = 2(2w + 6) + 2w\).
Simplify and solve the resulting equation for \(w\), then use the value of \(w\) to find \(l\) using \(l = 2w + 6\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Formulating Algebraic Expressions from Word Problems
This involves translating verbal descriptions into mathematical expressions or equations. For example, 'the length is 6 feet longer than twice the width' can be written as L = 2W + 6, where L is length and W is width.
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Introduction to Algebraic Expressions
Perimeter of a Rectangle
The perimeter of a rectangle is the total distance around it, calculated as P = 2(L + W), where L is length and W is width. This formula helps relate the dimensions to the given perimeter value.
Solving Linear Equations
Once the problem is expressed as an equation, solving linear equations involves isolating variables to find their values. This includes combining like terms and using inverse operations to solve for unknowns.
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Related Practice
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