/*! 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 18 Solve each equation. Check your ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 18

Solve each equation. Check your solution. $$11=\frac{b}{-3}$$

Short Answer

Expert verified
The solution is \(b = -33\). The check confirms it's correct.

Step by step solution

01

Multiply Both Sides by -3

To solve for \(b\) in the equation \(11 = \frac{b}{-3}\), we start by eliminating the fraction. Multiply both sides of the equation by \(-3\) to isolate \(b\) on one side. The equation becomes:\[11 imes (-3) = \frac{b}{-3} imes (-3)\]This simplifies to:\[-33 = b\]Now \(b\) is isolated.
02

Check the Solution

To ensure our solution is correct, substitute the value of \(b\) back into the original equation and verify if both sides are equal. The original equation is:\[11 = \frac{b}{-3}\]Substituting \(b = -33\) gives:\[11 = \frac{-33}{-3}\]This simplifies to:\[11 = 11\]Since both sides are equal, the solution \(b = -33\) 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.

Checking Solutions
Once you've proposed a solution to an equation, it鈥檚 vital to check whether it's correct. This ensures accuracy and helps prevent mistakes. To do this, substitute the calculated value back into the original equation and confirm both sides are equal. It's like a mini-test for your solution! For example, if you solved the equation \(11 = \frac{b}{-3}\) and found \(b = -33\), you should plug \(-33\) back into the equation:
  • Original Equation: \(11 = \frac{b}{-3}\)
  • Substituted Equation: \(11 = \frac{-33}{-3}\)
These steps should show both sides are equal, making sure your solution is correct. This practice not only reinforces confidence but helps you understand solving equations better. Remember, checking solutions is a key step in any math problem-solving process!
Fraction Elimination
Fractions can complicate equations by cluttering the arithmetic. A practical trick to simplify equations is to eliminate fractions early on. You do this by multiplying both sides by the denominator of the fraction, thereby simplifying the equation to a more manageable form.In the equation \(11 = \frac{b}{-3}\), the fraction \(\frac{b}{-3}\) is simplified by multiplying both sides by \(-3\):
  • Multiply both sides: \(11 \times (-3) = \frac{b}{-3} \times (-3)\)
  • Simplify: \(-33 = b\)
Through this method, the fraction is eliminated, and you're left with a straightforward equation that鈥檚 easier to work with. This step is crucial as it leads directly to the solution.
Equation Verification
Verifying an equation after solving it is like giving your solution a seal of confidence. This step involves double-checking your mathematical manipulations to ensure no mistakes were made.After finding a solution, revisit the problem to review each step:
  • Recalculate any arithmetic operations completed during solving.
  • Check each transformation, ensuring no rules of algebra were violated.
For example, in the problem \(11 = \frac{b}{-3}\), you verified \(b = -33\) by substituting back into the equation. If every action checks out, your solution stands confirmed. Being meticulous in equation verification can highlight careless errors and strengthen your understanding, giving you clarity and certainty in your work.

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

Find the next term in the pattern. $$20,22,26,32, \dots$$

Draw and label a rectangle that has a perimeter of 18 inches.

Name the quadrant in which \(P(-5,-6)\) is located.

Explain why formulas are important in math and science. Include an example of a formula from math or science that you have used and an explanation of how you used the formula.

Jake ran \(x\) miles on Monday, \(y\) miles on Tuesday, and \(z\) miles on Wednesday. Write an expression for the average number of miles Jake ran.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

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.