/*! 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 42 \(5 x=4 x+9\)... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 42

\(5 x=4 x+9\)

Short Answer

Expert verified
The solution is \(x = 9\).

Step by step solution

01

Isolate Variable Terms

First, we need to get all terms containing the variable on one side of the equation. Subtract \(4x\) from both sides to isolate \(x\) terms: \[5x - 4x = 4x + 9 - 4x\]
02

Simplify Both Sides

Simplify the left side and the right side: \[x = 9\]

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Key Concepts

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

isolating variables
To start solving the linear equation, we need to isolate the variable. This means getting the variable, in this case, \(x\), by itself on one side of the equation. This helps us see the relationship between \(x\) and the other numbers.
For example, if we look at the given exercise \(5x = 4x + 9\), our first step is to move all the terms that include \(x\) to one side.
We can do this by subtracting \(4x\) from both sides of the equation:
\[ 5x - 4x = 4x + 9 - 4x \]
Now, the equation becomes much simpler:
\[ x = 9 \]
By isolating the variable, we have made it clear that \(x\) equals 9. This is the simplest form of the equation.
simplifying equations
Once the variable is isolated, the next step is to simplify the equation. Simplifying means making the equation easier to understand and solve. This usually involves combining like terms and performing arithmetic operations.
In our example, we simplified the left side and the right side of the equation:
\[ 5x - 4x = 4x + 9 - 4x \]
Which simplifies to:
\[ x = 9 \]
Sometimes, simplifying the equation can involve more steps, like factoring or distributing, but in this case, it was straightforward: just basic subtraction. Always remember to perform the same operation on both sides of the equation to maintain the equality.
basic algebra
Solving linear equations is a fundamental skill in basic algebra. This involves understanding how to manipulate equations to find the value of the variable. Here are some key points to remember:
  • Always perform the same operation on both sides of the equation.
  • Combine like terms whenever possible.
  • Check your solution by plugging it back into the original equation.
In our example, the process was simple. We isolated the variable by subtracting \(4x\) from both sides and then simplified the equation to find \(x = 9\).
Basic algebra helps us understand how to balance equations and find unknown values. It's the foundation for more advanced math concepts and problem-solving skills.

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