/*! 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 329 In the following exercises, solv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 8: Problem 329

In the following exercises, solve each equation. $$ -8 x-15+9 x-1=-21 $$

Short Answer

Expert verified
x = -5

Step by step solution

01

Simplify like terms

Combine the like terms on the left side of the equation. This means combining -8x with 9x: -8x + 9x = x. Now, the equation is modified to: ewline x - 15 - 1 = -21.
02

Further simplification

Combine the constants on the left side of the equation: -15 - 1 = -16. Now, the equation looks like this: ewline x - 16 = -21.
03

Solving for x

Isolate the variable by adding 16 to both sides of the equation: x - 16 + 16 = -21 + 16. This simplifies to: ewline x = -5.

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
In solving linear equations, the first key step is to combine like terms. Combining like terms means grouping together the terms that have the same variable component. For example, in the equation given: \[-8x - 15 + 9x - 1 = -21\], you notice the terms \(-8x\) and \(9x\) both contain the same variable, \'x\'. To combine them, we add their coefficients (numbers in front the variables). Here's the math:
\(-8 + 9 = 1\).
So, \(-8x + 9x = x\). Now the equation simplifies to: \[x - 15 - 1 = -21\].
Combining like terms simplifies the equation, making it easier to solve.
Isolating variables
The next crucial step in solving equations is isolating the variable. Our goal is to get the variable by itself on one side of the equation. From our simplified equation: \[x - 15 - 1 = -21\], we first need to combine the constants (numbers without variables). So, \(-15 - 1 = -16\), which gives us: \[x - 16 = -21\]. Now we isolate the variable \(x\) by adding 16 to both sides:
\(x - 16 + 16 = -21 + 16\). This simplifies to \( x = -5 \).
Always remember to perform the same operation on both sides to maintain the balance of the equation.
Simplification
After combining like terms and isolating the variable, we often need to perform additional simplifications. Simplification means making the expression as simple as possible. In this example, let's review the simplification steps:
Step 1: Combine \(-8x+9x\) to get \(x\). This simplifies to: \(x-16 = -21\).
Step 2: To isolate \(x\), add 16 to both sides: \(x - 16 + 16 = -21 + 16\), which simplifies to \(x = -5\). Here we see the effect of all simplifications carried out in one smooth process. Simplification makes the equation easier to handle and ensures the logic is clear and step-by-step, bringing you closer to the solution: \(x = -5\).

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. Eva鈥檚 daughter is 5 years younger than her son. Eva鈥檚 son is 12 years old. How old is her daughter?

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

In the following exercises, solve each equation by clearing the fractions. $$ \frac{1}{3} x+\frac{1}{5} x=8 $$

In the following exercises, solve each equation. $$ 8(4 x+5)-5(6 x)-x=53 $$

In the following exercises, solve the equation. $$ 8(3 p+5)-23(p-1)=35 $$
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

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.