/*! 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 33 Solve each equation. $$ t+5=... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 33

Solve each equation. $$ t+5=20 $$

Short Answer

Expert verified
Answer: The value of t in the equation is 15.

Step by step solution

01

Identify the equation

The equation is given as: $$ t+5=20 $$
02

Isolate the variable t

Subtract 5 from both sides of the equation: $$ t+5-5=20-5 $$
03

Simplify

After subtraction, the equation simplifies to: $$ t=15 $$
04

Present the solution

The solution to the equation is: $$ t=15 $$

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.

Understanding Algebra
Algebra is a branch of mathematics that uses symbols to represent numbers and express mathematical relationships. In algebra, we often solve equations to find the values of unknown variables. In our exercise, the equation is a simple form of algebra that involves the variable \( t \). The goal is to determine the value of \( t \) such that the equation holds true. By using algebraic techniques, we convert the problem into a manageable form, allowing us to solve it logically and systematically. This often involves rearranging the equation and performing operations that simplify the expression.
Isolation of Variables
The process of isolation of variables is a key strategy in solving algebraic equations. This means rearranging the equation so that the variable you are solving for鈥攍ike \( t \) in our exercise鈥攊s on one side of the equation alone. Here, \( t+5=20 \) is transformed by subtracting the same value from both sides. This operation helps maintain the balance of the equation while getting \( t \) by itself. By isolating the variable, you make the problem much simpler to solve. Remember, whatever operation you do to one side, you must also do to the other. This ensures the equality is maintained. The result, in this case, is \( t = 15 \).
Mastery of Basic Arithmetic Operations
Basic arithmetic operations are the foundational skills required for working with algebraic equations. These include addition, subtraction, multiplication, and division鈥攅ach helping to manipulate equations into a solved state. In our example, subtraction was used to isolate \( t \). By subtracting 5 from both sides, \( t+5 = 20 \) simplifies to \( t = 15 \). Mastering these operations allows you to handle more complex equations with confidence. Arithmetic operations act as the essential tools necessary for algebraic problem-solving, enabling you to break down equations into simple steps to find the solution effortlessly.

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

In Problems \(52-55,\) decide whether the expressions can be put in the form $$ \frac{a x}{a+x} . $$ For those that are of this form, identify \(a\) and \(x\). $$ \frac{b^{2} \theta^{2}}{b^{2}+\theta^{2}} $$

In Exercises \(24-27,\) write an expression for the sales tax on car. $$ \text { Tax rate is } 6 \% \text { , price is } \$ 1000 \text { off the sticker price, } \$ p $$

In Exercises \(20-23,\) write an expression for the sequence of operations. $$ \text { Add } 3 \text { to } x \text { , subtract the result from } 1 \text { , double. } $$

It costs a contractor \(\$ p\) to employ a plumber, \(\$ e\) to employ an electrician, and \(\$ c\) to employ a carpenter. (a) Write an expression for the total cost to employ 4 plumbers, 3 electricians, and 9 carpenters. (b) Write an expression for the fraction of the total cost in part (a) that is due to plumbers. (c) Suppose the contractor hires \(P\) plumbers, \(E\) electricians, and \(C\) carpenters. Write expressions for the total cost for hiring these workers and the fraction of this cost that is due to plumbers.

Does the equation have a solution? Ex plain how you know without solving it. $$ 2+5 x=6+5 x $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

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.