/*! 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 13 Solve each equation. Check your ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 13

Solve each equation. Check your solution and graph it on a number line. $$a+10=-4$$

Short Answer

Expert verified
The solution is \(a = -14\).

Step by step solution

01

Isolate the Variable

To solve the equation \(a+10=-4\), we need to isolate \(a\). Subtract \(10\) from both sides of the equation to achieve this:\[ a + 10 - 10 = -4 - 10 \]Simplifying, we get:\[ a = -14 \]
02

Check the Solution

Plug the solution back into the original equation to ensure its accuracy. Substitute \(a=-14\) into the equation \(a+10=-4\):\[ -14 + 10 = -4 \]Simplifying the left side gives:\[ -4 = -4 \]Since both sides equal, the solution \(a = -14\) is correct.
03

Graph on a Number Line

To graph \(a = -14\) on a number line, draw a horizontal line and mark common integers such as \(-16, -15, -14, -13, -12, \) and so on. Place a point exactly on \(-14\) to represent the solution.

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
After finding a solution for an equation, it's crucial to check if it is indeed correct. This step confirms that our solution satisfies the original equation. To check a solution:
  • Substitute the solution back into the original equation.
  • Perform the arithmetic operations as indicated in the equation.
  • If both sides of the equation are equal after substitution, then the solution is verified.
In the case of the equation \( a + 10 = -4 \), we found that \( a = -14 \). Plugging \( -14 \) into the equation gives \( -14 + 10 = -4 \). Simplifying, we see that both sides become \( -4 \), confirming the solution is correct.
Checking solutions is essential because it prevents potential errors and assures us that the work done is accurate and reliable.
Number Line Graphing
Graphing an equation on a number line is a visual way to represent solutions. This method provides an easier understanding of where a solution lies concerning other numbers. Here is how you can graph \( a = -14 \):
  • Draw a horizontal line and evenly space markings to represent integers.
  • Label these markings with numbers such as \(-16, -15, -14, -13, \) and beyond, depending on space.
  • Place a distinct point, often a dot or a circle, at the coordinate representing the solution, which in this case is \(-14\).
Graphing helps in visualizing numbers in their context. It can also assist in understanding more complex math topics, such as inequalities and functions. A clearly drawn number line can highlight the position of solutions relative to other values.
Isolation of Variable
The method of isolation of the variable is fundamental in solving equations. It involves rearranging the equation so that the unknown variable is alone on one side of the equation, and all other terms are on the opposite side. The goal is to simplify the equation step by step. Here's how it works:
  • Identify the term containing the variable you want to solve for. In \( a + 10 = -4 \), the variable term is \( a \).
  • Perform the necessary arithmetic operations to both sides of the equation to get rid of other numbers near the variable. Here, subtract \( 10 \) from both sides to form \( a = -14 \).
This technique is not limited to addition or subtraction. Depending on the equation, one might need to use division, multiplication, or more advanced operations like logarithms or exponents. Mastering isolation of the variable is vital for solving algebraic equations of any form.

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

Use the following information. American Lance Armstrong won the 2005 Tour de France, completing the 2102 -mile race in 83 hours, 36 minutes, 2 seconds. Armstrong also won the 2003 Tour de France. He completed the 2125 -mile race in 80 hours, 2 minutes, 8 seconds. Without calculating, determine which race was completed with a faster average speed. Explain.

The table shows the number of people who took a cruise in various years. Make a scatter plot of the data. $$\begin{array}{|l|c|c|c|c|c|c|c|}\hline \text { Year } & 1997 & 1998 & 1999 & 2000 & 2001 & 2002 & 2003 \\\\\hline \text { Number (millions) } & 5.1 & 5.4 & 5.9 & 6.8 & 6.9 & 7.6 & 8.2 \\\\\hline\end{array}$$

Draw and label the dimensions of each rectangle whose perimeter and area are given. $$P=16 \mathrm{cm}, A=16 \mathrm{cm}^{2}$$

Use the Distributive Property to write each expression as an equivalent algebraic expression. $$(u-w)(-8)$$

Divide. $$-100 \div 10$$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

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.