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

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 11

Solve each equation. Check your solution and graph it on a number line. $$m+10=-2$$

Short Answer

Expert verified
The solution is \(m = -12\).

Step by step solution

01

Move Constants to the Other Side

To isolate the variable \(m\), we need to move the constant \(10\) to the other side of the equation. This is done by subtracting \(10\) from both sides: \(m + 10 - 10 = -2 - 10\).
02

Simplify the Equation

After subtracting \(10\) from both sides, the equation becomes \(m = -12\).
03

Check the Solution

Substitute \(m = -12\) back into the original equation to check if the solution is correct: \(-12 + 10 = -2\). This simplifies to \(-2 = -2\), confirming that \(m = -12\) is indeed a valid solution.
04

Graph Solution on a Number Line

Draw a number line and locate the point \(-12\). Since the solution is \(m = -12\), mark this point with a solid dot to show that \(-12\) is included in the solution set.

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
When solving linear equations, it's crucial to verify that your solution is correct. This process is known as "checking solutions". You achieve this by replacing the variable in the original equation with the solution you found. In our exercise, we determined that \( m = -12 \). To check this, substitute \( -12 \) back into the equation:
  • Start with the original equation: \( m + 10 = -2 \).
  • Substitute \( m \) with \( -12 \): \( -12 + 10 = -2 \).
  • Calculate the left side: \( -12 + 10 = -2 \).
  • Compare both sides: \( -2 = -2 \).
The equation holds true, so \( m = -12 \) is indeed the correct solution. This step reinforces confidence in your solution and ensures no careless mistakes were made.
Number Line Graphing
Graphing a solution on a number line is a visual way to represent your findings. It helps in understanding where the solution lies in relation to other numbers. Here's how you perform number line graphing for our solution, \( m = -12 \):
  • First, draw a horizontal line and mark it at equal intervals.
  • Identify the position of zero on this line, then find \( -12 \) by counting segments to the left.
  • Once you've located \( -12 \), mark this number with a solid dot.
The solid dot signifies that \( m = -12 \) is included in the solution set. This visual aid can help you see the solution distribution, and it's especially useful when dealing with inequalities.
Integer Operations
Integer operations are fundamental in solving linear equations, as they involve adding and subtracting whole numbers. Let's look at how these operations helped solve our equation:
  • We began with \( m + 10 = -2 \). Our first task was to isolate \( m \), and to do this, we subtracted \( 10 \) from both sides. Subtraction is one of the primary operations on integers.
  • Performing \( 10 - 10 = 0 \) on the left side helped us eliminate the constant next to \( m \).
  • On the right side, \( -2 - 10 \) was simplified to \( -12 \) with basic subtraction.
In linear equations, often all you need are integer operations to isolate variables and find solutions. Mastering these operations can greatly ease the process of solving not just equations, but a wide range of mathematical problems.

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

Evaluate \(\frac{-4 y}{x}\) if \(x=2\) and \(y=-3\).

Each participant in a community garden is allotted a rectangular plot that measures 18 feet by 45 feet. How much fencing is needed to enclose each plot?

Simplify each expression. $$2(x+6)+4 x$$

Jordan is paving a rectangular patio with bricks. If the patio contains a total of 308 bricks and there are 22 bricks running along the length of the patio, how many bricks run along the width of the patio?

Find the next term in the pattern. $$5,9,13,17, \dots$$
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

Read Explanation

Statistics

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.