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Chapter 2: Problem 25

Solve using the addition principle. Don't forget to check! $$ x-8=5 $$

Short Answer

Expert verified
x = 13

Step by step solution

01

Understand the Problem

We need to solve the equation \(x - 8 = 5\) using the addition principle. The goal is to isolate \(x\).
02

Add 8 to Both Sides

To isolate \(x\), add 8 to both sides of the equation: \(x - 8 + 8 = 5 + 8\)
03

Simplify Both Sides

Simplify the equation by performing the addition: \(x = 13\)
04

Check the Solution

Substitute \(x = 13\) back into the original equation to verify: \(13 - 8 = 5\), which is true. So the solution is correct.

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Key Concepts

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

Understanding the Addition Principle
The addition principle is an essential concept in solving equations. It states that you can add the same number to both sides of an equation without changing its equality. This is crucial for isolating the variable we want to solve for.

In the exercise, we have the equation:
\( x - 8 = 5 \)

Our goal is to isolate the variable \( x \). By adding 8 to both sides of the equation, we use the addition principle to keep the equation balanced. Here's how it looks:
\( x - 8 + 8 = 5 + 8 \)

Adding 8 to \( x - 8 \) eliminates the -8, leaving:
\( x = 13 \)
This shows \( x \) isolated and thus, we have identified its value.
Isolating the Variable
Isolating the variable means getting the variable (here, \( x \)) by itself on one side of the equation. This process helps us find the value of the unknown.

In our exercise, we start with:
\( x - 8 = 5 \)

To isolate \( x \), use the addition principle. Add 8 to both sides:
\( x - 8 + 8 = 5 + 8 \)

This simplifies to:
\( x = 13 \)
Now, \( x \) is isolated on the left side, and its value is clear.

Always remember, whatever operation you apply to one side of the equation must be done equally to the other side to maintain equality.
Checking Solutions
Checking solutions is an important step to ensure that our solved variable is correct. This verifies that our solution meets the original equation.

For the solved value: \( x = 13 \)
Substitute \( x \) back into the original equation:
\( 13 - 8 = 5 \)

Simplify the left side to see if it equals the right side:
\( 5 = 5 \)

Since both sides of the equation are equal, our solution is verified to be correct. Always perform this check to ensure the solution is valid and accurate.

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