/*! 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 24 In the following exercises, solv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 24

In the following exercises, solve each equation. $$ 9 x+5-8 x+14=20 $$

Short Answer

Expert verified
x = 1

Step by step solution

01

Combine Like Terms

Simplify the equation by combining like terms on the left side, which are the terms with the variable x. So, combine 9x and -8x.
02

Simplify the Equation

After combining the like terms, the equation becomes: 1x + 19 = 20. Then, simplify it to x + 19 = 20
03

Isolate the Variable

Subtract 19 from both sides of the equation to isolate the variable x. x + 19 - 19 = 20 - 19
04

Solve for x

After simplifying both sides, the equation becomes: x = 1

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.

Combining Like Terms
To solve linear equations, one of the first steps is to combine like terms. Like terms are terms in an equation that have the same variable raised to the same power. In the equation provided, there are two terms that contain the variable x: \(9x\) and \(-8x\).
By combining these, we add the coefficients (the numbers in front of the x) together, while keeping the variable x.
  • \(9x + (-8x) = 1x\)
Therefore, the equation simplifies to \(1x + 19 = 20\). When the variable terms are combined, it makes the equation more manageable and easier to solve. Always remember: combining like terms is crucial for simplifying the equation effectively.
Isolating the Variable
After combining like terms, the next key step is isolating the variable. Our goal here is to get the variable, in this case x, all by itself on one side of the equation. This makes it possible to determine its value easily. In the equation from the exercise, we have: \( x + 19 = 20 \)
  • To isolate x, we need to remove the 19 that is added to x
  • We do this by performing the opposite operation, which is subtraction
  • Subtract 19 from both sides of the equation: \( x + 19 - 19 = 20 - 19 \)
This results in \( x = 1 \). By isolating the variable, we've taken a big step towards solving the equation.
Simplifying Equations
Simplifying equations is a process that involves making an equation as straightforward as possible. This often involves combining like terms and isolating the variable as we discussed earlier. By simplifying an equation, we eliminate any unnecessary terms and reduce the problem to its most basic form. For instance, in the initial equation: \(9x + 5 - 8x + 14 = 20\),
we combined like terms to get \(1x + 19 = 20 \). Then, we isolated the variable. The steps to simplify can vary, but generally include:
  • Combining like terms
  • Removing any constants or coefficients that clutter the equation
  • Isolating the variable
Each of these simplifying steps brings us closer to finding the solution in an organized, systematic way. Simplifying makes solving linear equations easier and more efficient.

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

In the following exercises, translate into an equation and solve. Pilar drove from home to school and then to her aunt鈥檚 house, a total of 18 miles. The distance from Pilar鈥檚 house to school is 7 miles. What is the distance from school to her aunt鈥檚 house?

In the following exercises, solve each equation by clearing the fractions. $$ \frac{3}{4} a-\frac{1}{3}=\frac{1}{2} a+\frac{5}{6} $$

Is \(-18\) a solution to the equation \(3 x=16-5 x ?\) How do you know?

In the following exercises, translate to an equation and then solve. Ten less than \(m\) is \(-14\)

In the following exercises, solve each linear equation using the general strategy. $$ 5+7(2-5 x)=2(9 x+1)-(13 x-57) $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Probability and Statistics

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.