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Chapter 2: Problem 10

\(x-9=8\)

Short Answer

Expert verified
x = 17

Step by step solution

01

- Understand the Equation

The given equation is a simple linear equation: \(x - 9 = 8\). The goal is to solve for the variable \(x\).
02

- Isolate the Variable

To isolate \(x\), add 9 to both sides of the equation to undo the subtraction: \((x - 9) + 9 = 8 + 9\).
03

- Simplify the Equation

Simplify both sides of the equation: \(x = 17\).
04

- Verify the Solution

Double-check the solution by substituting \(x = 17\) back into the original equation: \(17 - 9 = 8\), which is true.

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Key Concepts

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

Isolating the Variable
When solving linear equations, our main goal is to find the value of the unknown variable, in this case, x. To achieve this, we need to 'isolate the variable.' This means we should get the variable alone on one side of the equation. For the equation given:
x - 9 = 8
We need to undo the subtraction of 9 to isolate x. We do this by adding 9 to both sides of the equation. This keeps the equation balanced and helps us get x by itself.
So, we perform:
(x - 9) + 9 = 8 + 9
By adding 9 to both sides, the left side simplifies to just x, effectively isolating the variable as we wanted.
Simplification
Simplification is the process of reducing the equation to its simplest form to find the value of the isolated variable. After isolating x, we have the equation:
x + 0 = 17
We then remove the zero to simplify further:
x = 17
This is a simple process, but every step is important to ensure our final answer is correct. Simplification makes equations more understandable and easier to work with.
Verification of Solution
After finding a solution, it is crucial to verify that it is correct. Verification ensures that the solution we obtained satisfies the original equation. In our case, the solution is x = 17. To verify, substitute x back into the original equation:
17 - 9 = 8
As both sides of the equation are equal, our solution is correct. This step helps us confirm our work and guarantees we've solved the problem properly. Always double-check your solutions as a good practice.

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