/*! 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 336 In the following exercises, solv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 336

In the following exercises, solve. $$ b-1=11 $$

Short Answer

Expert verified
b = 12

Step by step solution

01

Understand the Equation

The given equation is: \( b - 1 = 11 \). Here, the task is to find the value of the variable \( b \).
02

Isolate the Variable

To isolate \( b \), add 1 to both sides of the equation. This is done to cancel out the -1 on the left side. \[ b - 1 + 1 = 11 + 1 \]
03

Simplify the Equation

Simplify both sides of the equation. The left side simplifies to \( b \) and the right side to 12. \[ b = 12 \]

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.

isolating variables
Isolating variables means we want to get the variable we are solving for by itself on one side of the equation. In the given exercise, our goal was to isolate the variable \( b \). To do this, follow these steps:

First, identify what operations are being performed on the variable. In our equation, \( b - 1 = 11 \), the variable \( b \) is being subtracted by 1. To isolate \( b \), we need to undo this operation.

To cancel out \(-1\) next to \( b \), we do the opposite operation, which is addition. We add 1 to both sides of the equation:

  • \tLeft side: \(b - 1 + 1 = b\)
  • \tRight side: \(11 + 1 = 12\)
The variable \( b \) is now isolated, making it easy to see that \( b = 12 \).
simplifying equations
Simplifying equations involves reducing the equation to its simplest form so that the solution becomes clear. After isolating the variable, the equation must be simplified where needed. In this exercise, we simplified the left and right sides after adding 1 to both sides:

The initial adjustment was: \( b - 1 + 1 = 11 + 1 \).

  • \tOn the left side: \(b - 1 + 1\) simplifies to just \( b \).
  • \tOn the right side: \( 11 + 1 \) simplifies to 12.
Thus, the simplified equation is \( b = 12 \). This simplification step is crucial because it ensures that the variable is isolated neatly, and the solution is straightforward.
basic algebra
Basic algebra forms the foundation for solving more complex math problems. It is essential to understand a few fundamental concepts and operations. In our problem, these concepts guided us to find the solution efficiently.

  • \t**Variables**: Symbols like \( b \) that represent unknown values.
  • \t**Operations**: Actions like addition or subtraction that are applied to variables and numbers.
  • \t**Equations**: Mathematical statements that show the equality between two expressions.
  • \t**Isolating Variables**: Steps to get the variable alone on one side of the equation (covered in the first section).
  • \t**Simplification**: Reducing the equation to its simplest form (explained in the second section).
In this exercise, our equation, \(b - 1 = 11\), showcased these basic concepts. We manipulated the equation using the principles of basic algebra to find our answer. Therefore, understanding these fundamentals empowers us to solve a wide range of linear equations effectively.

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 the following exercises, solve the given applications. $$ -1 \cdot 6 $$

In the following exercises, evaluate. $$ 35-a \text { when } a=-4 $$

In the following exercises, simplify each expression. $$ (-2)^{5} $$

In the following exercises, simplify. $$ -8+6 $$

In the following exercises, divide. $$ 45 \div(-1) $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Logic and Functions

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.