/*! 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 11 Is \(-6\) a solution of \(-2 x+3... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 11

Is \(-6\) a solution of \(-2 x+3=15 ?\)

Short Answer

Expert verified
Yes, \(-6\) is a solution.

Step by step solution

01

Substitute -6 into the equation

First, substitute the value \(x = -6\) into the equation \(-2x + 3 = 15\). This results in: \(-2(-6) + 3 = 15\).
02

Evaluate the multiplication

Now, simplify inside the parentheses by performing the multiplication:\(-2 imes (-6) = 12\).The equation now becomes:\(12 + 3 = 15\).
03

Simplify the expression

Next, add the numbers on the left side of the equation:\(12 + 3 = 15\).The equation simplifies to:\(15 = 15\).
04

Verify equality

Finally, verify if both sides of the equation are equal. In this case, they are:\(15 = 15\). This confirms that \(-6\) is a solution to the equation.

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.

Substitution Method
The substitution method is a powerful technique used to solve equations. In simple terms, it involves replacing a variable with a given number to find out whether it satisfies the equation. Let's take a look at how this works with the example of determining if \(-6\) is a solution to the equation \(-2x + 3 = 15\).
  • The first step is to replace \(x\) with the number \(-6\). So, wherever you see \(x\) in the equation, substitute it with \(-6\).
  • This changes the original equation \(-2x + 3 = 15\) into \(-2(-6) + 3 = 15\).
By substituting the variable with a specific value, you simplify the process to check if the given number truly solves the equation.
Evaluating Expressions
Evaluating expressions is basically calculating the result of an equation after substituting the variables with numbers. In our example where we've substituted \(-6\) into \(-2x + 3 = 15\), we need to do some simple arithmetic to see if the equation holds true.
  • Start by handling the multiplication: \(-2 \times (-6)\). Remember, multiplying two negative numbers results in a positive number: thus, \(-2 \times (-6) = 12\).
  • Next, continue by adding the result to 3: \(12 + 3\).
  • This results in 15 on the left side of the equation, making it \(15 = 15\). The expression holds true.
Evaluating expressions is a crucial step in determining whether a value is a solution to the equation. It involves performing basic arithmetic operations to simplify parts of the equation until you can verify the answer.
Verifying Solutions
Verifying solutions is the final step where you make sure that the number you've substituted is indeed a true solution to the equation. In this context, it is about checking whether the left side of the equation equals the right side after having evaluated all necessary expressions.
  • Once you've substituted \(-6\) and evaluated the expression, the equation simplifies to \(15 = 15\).
  • This shows both sides of the equation are equal, thereby confirming that \(-6\) is the correct solution.
  • If both sides were not equal, it would mean \(-6\) was not a solution to the equation.
Verifying your solution ensures that the equation holds true, guaranteeing the correctness of your calculations. It's a key step to confirm that your substitution and evaluation were carried out correctly.

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

Simplify the given expression. \(\frac{-6.9-(-4)}{2}\)

. The quotient of two integers is 3 . One of the integers is \(-7\). Find the other integer.

Solve the given equation for \(\mathrm{x}\). \(15 x-2=43\)

Solve the given equation for \(\mathrm{x}\). \(\frac{x}{-8}=-1\)

Solve the given equation for \(x\). \(x-3=6\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

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.