/*! 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 12 Solve the equations by using the... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 12

Solve the equations by using the subtraction property. $$x+8=19$$

Short Answer

Expert verified
The solution to the equation is \( x = 11 \).

Step by step solution

01

Identify the Equation

We need to solve the equation \( x + 8 = 19 \). Our goal is to isolate \( x \) on one side of the equation to find its value.
02

Apply the Subtraction Property

To isolate \( x \), subtract 8 from both sides of the equation. This is because the subtraction property of equality allows us to maintain balance by performing the same operation on both sides of the equation.\[ x + 8 - 8 = 19 - 8 \]
03

Simplify the Equation

After applying the subtraction property, simplify both sides. On the left side, \( 8 - 8 = 0 \), which leaves us with:\[ x = 19 - 8 \]
04

Calculate the Result

Complete the subtraction on the right side to find the value of \( x \):\[ x = 11 \]

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.

Subtraction Property of Equality
The subtraction property of equality is a fundamental principle in solving equations. It allows us to subtract the same number from both sides of an equation, helping to maintain the balance of the equation. Imagine the equation as a perfectly balanced scale. By subtracting an equal value from both sides, the scale remains balanced.
The important thing to remember is that whatever operation you perform on one side, you must also do on the other. This keeps the equation true, and it does not change the solution.
  • For example, in the equation \( x + 8 = 19 \), subtracting 8 from both sides gives you \( x = 19 - 8 \). The balancing principle is preserved.
This approach is very reliable and helps us successfully manipulate and solve equations.
Isolating Variables
Isolating the variable is a key step in solving any equation. Our goal is to get the variable by itself on one side of the equation. This allows us to easily determine its value.
In the example \( x + 8 = 19 \), we want to isolate \( x \). By using the subtraction property of equality and subtracting 8 from both sides, we are effectively isolating \( x \).
  • This means that after the operation, only \( x \) remains on the left side: \( x = 11 \).
By following these steps, you can simplify even complex equations, focusing on gradually getting the variable alone. This technique simplifies understanding and ensures that your final answer makes sense.
Simplifying Equations
Simplifying equations is the process of making an equation easier to read and solve. It generally involves combining like terms and eliminating any extra steps that complicate the equation.
In the equation \( x + 8 - 8 = 19 - 8 \), simplifying means doing the subtraction on both sides.
  • The left side simplifies by removing the +8 and -8 (which equal zero), leaving us with just \( x \).
  • The right side simplifies to 11 after subtracting 8 from 19.
Simplification helps you clearly see the solution. By methodically reducing each step, solving equations becomes straightforward and less daunting. Always aim for simplicity in your calculations to ensure accuracy.

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

Consider the formula $$\frac{0.55-p}{\sqrt{\frac{p(1-p)}{n}}}$$ Evaluate this expression using the given values. Round the results to three decimal places. $$p=0.65, n=59$$

Solve the equations. More than one step is needed in each case.$$-2-3 x=-20$$

Use the formula $$A=\pi d^{2}$$ for the surface area \(A\) of a sphere whose diameter measures \(d\). This formula yields the surface area in square units. Round the results to three decimal places and include proper units. The Hoberman Sphere is a mechanical toy that expands from 5.9 inches in diameter when it is fully closed, to 30.1 inches in diameter when fully expanded. What is the difference in the surface area of a Hoberman sphere from when it is fully closed to when it is fully expanded?

Consider the formula $$\frac{x-50}{\frac{s}{\sqrt{n}}}$$ Evaluate this expression using the given values. Round the results to two decimal places. $$x=50.5, s=6.3, n=30$$

Apply the order of operations and answer the questions. The area of a circle of radius 11 inches is given by the expression \(\pi(11)^{2}\). Evaluate the expression and interpret the answer by rounding the result to one decimal place.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

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.