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Chapter 2: Problem 16

Solve each linear equation. Show your work and check your answer. $$x-5=12$$

Short Answer

Expert verified
x = 17

Step by step solution

01

Isolate the variable

To find the value of the variable, isolate it on one side of the equation. Add 5 to both sides of the equation: \(x - 5 + 5 = 12 + 5\)
02

Simplify the equation

Simplify both sides of the equation: \(x = 17\)
03

Check the solution

Substitute the solution back into the original equation to verify it is correct. Replace \(x\) with 17: \(17 - 5 = 12\). Since both sides are equal, \(x = 17\) is correct.

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Key Concepts

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

variable isolation
When solving a linear equation, the first step is to isolate the variable. This process means getting the variable (like x) alone on one side of the equation. In the equation given, \( x - 5 = 12 \), we want to solve for x. To do this, think about getting rid of everything around x. Here, since we have -5 with x, we need to add 5 to both sides to cancel out the -5. This step gives us: \( x - 5 + 5 = 12 + 5 \). The -5 and +5 cancel each other out, so the equation simplifies to:\( x = 17 \). Now, x is isolated, and we've successfully completed the first step!
equation simplification
After isolating the variable, the next step is to simplify the equation. Simplification involves performing arithmetic operations to reduce the equation to its simplest form. After adding 5 to both sides in the previous step, the equation became \( x = 17 \). There are no more terms to combine or simplify, so this is our final simplified equation. Simplification helps us clearly see the value of the variable. It ensures that the equation is easy to read and understand.
solution verification
Once we have found the solution, it's important to verify if it's correct. Verification means plugging the solution back into the original equation to check if both sides are equal. For our equation \( x - 5 = 12 \), we substitute x with 17:\( 17 - 5 = 12 \). Since both sides of the equation match, this means our solution is correct. Verifying your solution helps confirm that you have solved the equation accurately. It is a crucial step to avoid errors.

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