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Chapter 2: Problem 26

Solve each equation, and check your solution. $$ x-15.5=-5.1 $$

Short Answer

Expert verified
The solution to the equation is \( x = 10.4 \).

Step by step solution

01

Isolate the variable

Add 15.5 to both sides of the equation to isolate the variable \(x\). This will give you: \[ x - 15.5 + 15.5 = -5.1 + 15.5 \]
02

Simplify the equation

Simplify the equation by performing the addition on both sides. This results in: \[ x = 10.4 \]
03

Check the solution

To verify the solution, substitute \( x = 10.4 \) back into the original equation: \[ 10.4 - 15.5 = -5.1 \]. Since both sides of the equation are equal, 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
Isolating the variable is a key step in solving linear equations. This means rearranging the equation to get the variable by itself on one side. For instance, in our example, the equation is \( x - 15.5 = -5.1 \). Here, we aim to isolate \(x\) by removing \( -15.5 \) from the left side. We do this by performing the opposite operation, which is addition, to both sides of the equation.

So, we add \( 15.5 \) to both sides:

\[ x - 15.5 + 15.5 = -5.1 + 15.5 \]

This helps us isolate \(x\), making the variable stand alone on one side of the equation, which leads us to the next step of simplification.
Simplification
After isolating the variable, the next step is to simplify the equation. Simplification involves performing the arithmetic operations to reduce the equation further. In our example, simplifying the equation \[ x - 15.5 + 15.5 = -5.1 + 15.5 \] means adding \( 15.5 \) on the right side:

\[ -5.1 + 15.5 = 10.4 \].

Therefore, we can say that:

\[ x = 10.4 \]

Simplification is crucial because it reduces the equation to its most basic form, making it easier to see the solution clearly.
Verification of Solution
Verification of the solution is the final step to ensure the accuracy of our answer. To verify, substitute the solution back into the original equation and see if both sides of the equation are equal. In this case, we substitute \( x = 10.4 \) back into \( x - 15.5 = -5.1 \).

Performing the substitution:

\[ 10.4 - 15.5 = -5.1 \],

Since \[ 10.4 - 15.5 = -5.1 \], the left side equals the right side. This confirms that our solution, \( x = 10.4 \), is indeed correct.

Verification is essential, as it provides confidence that the solution is accurate and satisfies the original equation.

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