/*! 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 85 Solve each equation. Then check ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 85

Solve each equation. Then check the result. $$ 23 b=23 $$

Short Answer

Expert verified
The solution is \(b = 1\).

Step by step solution

01

Understand the Equation

The equation given is a linear equation: \(23b = 23\). It means that the product of 23 and some number \(b\) is 23.
02

Isolate the Variable

To solve for \(b\), divide both sides of the equation by 23: \(b = \frac{23}{23}\).
03

Simplify the Expression

Simplify \(\frac{23}{23}\). Since \(23\) divided by \(23\) gives \(1\), the equation simplifies to: \(b = 1\).
04

Verify the Solution

To verify the solution, substitute \(b = 1\) back into the original equation: \(23 \times 1 = 23\). This is true, confirming our solution is correct.

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 Equations
Solving equations is the process of finding the value of the unknown variable that makes the equation true. In this exercise, we have a simple linear equation:
  • A linear equation is one where the highest power of the variable is one.
  • In a linear equation like \(23b = 23\), the goal is to determine the number \(b\) that, when multiplied by 23, results in 23.
We face a straightforward challenge, but it lays the foundation for understanding more complex equations later. The key to solving linear equations is to perform operations that maintain the balance of the equation, allowing us to isolate the variable. By systematically applying inverse operations, we can efficiently solve for the unknown.
Isolate the Variable
Isolating the variable is a crucial step in solving equations and means getting the variable by itself on one side of the equation. Here's how it works:
  • Begin by identifying the operations affecting the variable. For \(23b = 23\), the operation is multiplication by 23.
  • Use the inverse operation to cancel this out. Since the equation involves multiplication, we use division as the inverse operation.
  • Divide both sides of the equation by 23 to get: \(b = \frac{23}{23}\).
Once you've divided, the expression simplifies to \(b = 1\). Isolating the variable is often the key step, as it brings us one step closer to the solution. Remember, every operation you perform on one side must be done to the other to maintain equality.
Verify Solution
Verifying the solution confirms that the value found for the variable is correct. After solving an equation, always plug the solution back into the original equation to ensure it satisfies it.
  • Substitute the solved value of \(b\), which is 1, back into the original equation: \(23 \times 1 = 23\).
  • Check that both sides of the equation are equal. In this case, they are, so the solution is verified.
Verifying is like double-checking your work and prevents errors. It gives you confidence that your solution is correct. Whether dealing with simple or complex equations, this step is essential to ensure accuracy and reliability.

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

Solve each inequality or compound inequality. Write the solution set in interval notation and graph it. $$ 3(3 x+3)-2 \leq 2(2 x-1)+6 x $$

Solve each inequality or compound inequality. Write the solution set in interval notation and graph it. $$ \frac{11}{9} x>\frac{5}{9} $$

Geometry. The perimeter of a square is no less than 68 centimeters. How long can a side be?

What percent of 200 is \(30 ?\)

Multiply. $$ \frac{1}{2}(4 b-8) $$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Mechanics 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.