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Chapter 2: Problem 15

Solve each linear equation. Show your work and check your answer. $$x+3=24$$

Short Answer

Expert verified
x = 21. Verified by substituting back into the original equation.

Step by step solution

01

- Isolate the variable

Subtract 3 from both sides of the equation to isolate the variable x. Given: x + 3 = 24 becomes x + 3 - 3 = 24 - 3
02

- Simplify both sides

Simplify the equation by performing the subtraction: x = 21
03

- Check your solution

Substitute the value of x back into the original equation to verify the solution. Substitute: x = 21 into x + 3 = 24 becomes 21 + 3 = 24 which simplifies to 24 = 24, confirming the solution is correct.

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Key Concepts

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

Isolate the Variable
When solving linear equations, the first step is often to 'isolate the variable'. This means getting the variable by itself on one side of the equation.
In our example, we started with the equation \(x + 3 = 24\). To isolate \(x\), we need to remove the +3.
To do this, perform the inverse operation. Since +3 is a positive term, subtracting 3 from both sides of the equation will cancel it out.
Hence, the equation becomes \(x + 3 - 3 = 24 - 3\). Since \(+3 - 3 = 0\), we are left with \(x = 21\).
This process helps us focus only on the variable, which is critical for finding the correct value.
Simplify Equations
The next step is to simplify the equation. Simplification is about making the equation as straightforward as possible.
In our original equation, after isolating the variable, we ended up with \(x = 21\).
Here, the equation didn't need further simplification because it already presented the solution clearly.
However, more complex equations might require additional steps like combining like terms or reducing fractions.
Simplification makes it easier to understand and work with the equation.
Check the Solution
The final step in solving linear equations is to 'check the solution'. This step ensures your answer is correct.
To verify, substitute the found value back into the original equation. In our case, substitute \(x = 21\) back into \(x + 3 = 24\).
Performing the substitution gives us \(21 + 3 = 24\), which simplifies to \(24 = 24\).
Since both sides of the equation are equal, the solution is confirmed correct.
Always check your work; it's a good habit that ensures accuracy and reinforces understanding.

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