/*! 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 14 \(x-5=-7\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 14

\(x-5=-7\)

Short Answer

Expert verified
The solution is \( x = -2 \).

Step by step solution

01

- Identify the Equation

The given equation is: \[ x - 5 = -7 \]
02

- Add 5 to Both Sides

To isolate the variable \( x \), add 5 to both sides of the equation: \[ x - 5 + 5 = -7 + 5 \]
03

- Simplify Both Sides

Simplify the equation: \[ x = -2 \]

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.

Isolate the Variable
When solving linear equations, one primary goal is to isolate the variable. This means getting the variable on one side of the equation by itself. For instance, in the given problem: The equation is: To isolate the variable (in this case, it is x), we need to remove any constants or coefficients attached to it. Start by focusing on getting rid of the -5. Since we want to solve for x, everything else must be moved to the other side of the equation.
Addition Property of Equality
The addition property of equality is a fundamental rule in algebra. This property states that if you add the same number to both sides of an equation, the equation remains balanced. Here鈥檚 how it works with our given problem: To move the -5 from the left side of the equation, we can add 5 to both sides. Remember, whatever you do to one side, you must do to the other. This gives us: Now you can see how adding the same value to both sides helps to maintain the balance of the equation while progressing towards isolating the variable x.
Simplification
Simplification is the process of making an equation easier to solve. After applying the addition property of equality, the next step is to simplify both sides of the equation. Let鈥檚 take a closer look at our equation: After adding 5 to both sides, we get: Simplify the right side by performing the addition: -7+5 = -2. Therefore, we now have: This confirms that x is isolated, and the variable equals -2. Always check your work by substituting the value back into the original equation to ensure it balances. In this instance, substituting x = -2 back into: x - 5 gives us: which holds true, verifying our solution is correct.

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 measure of an angle whose supplement is three times its measure.

To see the connection between the solution of an equation and the solutions of the corresponding inequalities. Solve the following equation, and graph the solution set on a number line. \(3 x+2=14\)

The United States earned 121 medals at the 2016 Summer Olympics. The number of silver medals earned was 1 fewer than the number of bronze medals. The number of gold medals earned was 8 more than the number of bronze medals. How many of each kind of medal did the United States earn? (Data from The World Almanac and Book of Facts.)

When \(\frac{2}{3}\) of a number is added to \(10,\) the result is 5 more than the number. Find the number.

Find two consecutive odd integers such that twice the greater is 17 more than the lesser.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

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.