/*! 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 64 \(7 x-8-6 x=4\)... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 64

\(7 x-8-6 x=4\)

Short Answer

Expert verified
x = 12

Step by step solution

01

Combine Like Terms

Simplify the left side of the equation by combining the terms that contain the variable x: \[7x - 6x - 8 = 4\].
02

Simplify the Expression

Combine the x terms on the left side: \[(7 - 6)x - 8 = 4\]. This simplifies to: \[x - 8 = 4\].
03

Isolate the Variable

Add 8 to both sides of the equation to isolate the variable x: \[x - 8 + 8 = 4 + 8\]. This simplifies to: \[x = 12\].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

combining like terms
When solving linear equations, one of the initial steps often involves combining like terms. Like terms are terms that contain the same variable raised to the same power. In the equation \(7x - 8 - 6x = 4\), the terms \(7x\) and \(-6x\) are like terms because both contain the variable \(x\). To combine them, simply add or subtract their coefficients (the numerical part in front of the variable).In this example, we combine \(7x\) and \(-6x\): \(7x - 6x = (7 - 6)x = x\). After combining these terms, the equation simplifies to \(x - 8 = 4\)
simplifying expressions
Simplifying expressions means to make the expression easier to work with by combining like terms and performing basic arithmetic operations. In the simplified form of our equation, \textt{x - 8 = 4}\(, there's not much to simplify anymore. But before reaching this stage, we simplified the left side from \texttt{7x - 8 - 6x}\) to \( x - 8\). Always ensure that you've combined all like terms and simplified fully. This makes it easier to see the steps needed to isolate the variable.
isolating the variable
To find the value of the variable, we isolate it on one side of the equation. This means we want \(x\) alone on one side of the equation. In the simplified equation \(x - 8 = 4\), we need to get rid of the \(-8\) next to \(x\). To do this, we perform the opposite operation: add 8 to both sides:
  • \(x - 8 + 8 = 4 + 8\)
  • \(x = 12\)
Now, \(x\) is alone on one side, and we have \(x = 12\). This is the solution to the equation. Always check your work by substituting the solution back into the original equation to ensure it satisfies the equation.

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