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Chapter 2: Problem 31

\(-4=x-14\)

Short Answer

Expert verified
x = 10

Step by step solution

01

- Isolate the Variable

Add 14 to both sides of the equation to isolate the variable on one side. This will give you \(-4 + 14 = x - 14 + 14\).
02

- Simplify Both Sides

Combine the numbers on the left side. \(-4 + 14 = 10\). So, the equation becomes \(10 = x\).
03

- Verify the Solution

To ensure the solution is correct, substitute \(x = 10\) back into the original equation and verify: \(-4 = 10 - 14\), which simplifies to \(-4 = -4\), 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.

Isolating the Variable
When solving linear equations, the goal is often to isolate the variable on one side of the equation. This means getting the variable by itself. In the exercise, we started with \(-4 = x - 14\). To isolate \x\, we need to move \-14\ to the other side.

To do this, we add 14 to both sides. Remember, whatever you do to one side, you must do to the other to keep the equation balanced. So, we perform the operation like this:
  • Add 14 to both sides: \(-4 + 14 = x - 14 + 14\)
  • Combine like terms to simplify: \10 = x\
Now, we've successfully isolated \x\, and our equation is much simpler.
Simplifying Equations
Simplifying equations involves combining like terms and reducing the equation to its simplest form. After isolating the variable, our equation was \(-4 + 14 = x - 14 + 14\).

The next step is to combine the numbers on the left side of the equation.
  • Simplify \-4 + 14\ to get 10
  • Now, our simplified equation reads: \10 = x\
This means \x\ is 10. Simplifying makes it easier to see the value of the variable.
Verifying Solutions
It's essential to verify your solutions to ensure they're correct. You do this by plugging the solution back into the original equation.

For our problem, we found \x = 10\. Let's substitute 10 back into the original equation \(-4 = x - 14\):
  • Replace \x\ with 10: \(-4 = 10 - 14\)
  • Simplify the right side: \(10 - 14 = -4\)
We see that both sides of the equation are equal, \(-4 = -4\), so our solution is verified. Verifying confirms that we didn't make any errors while solving.

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