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Chapter 2: Problem 28

Solve each equation, and check your solution. $$ x+21.5=-13.4 $$

Short Answer

Expert verified
x = -34.9

Step by step solution

01

Isolate the Variable

To isolate the variable, subtract 21.5 from both sides of the equation. This will help us find the value of x.\( x + 21.5 - 21.5 = -13.4 - 21.5 \)
02

Simplify

Simplify both sides of the equation to solve for x. The left side simplifies to just x and the right side becomes the sum of -13.4 and -21.5.\( x = -34.9 \)
03

Check the Solution

Substitute the value of x back into the original equation to verify the solution:\( x + 21.5 = -13.4 \)\( -34.9 + 21.5 = -13.4 \)\( -13.4 = -13.4 \)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
In solving linear equations, isolating the variable is often the first step. This means rearranging the equation so that the variable, often denoted as \(x\), is on one side and everything else is on the other side.
To isolate the variable, we typically use inverse operations. In the given exercise, the equation is: \(x + 21.5 = -13.4\)
We need to get \(x\) by itself on one side of the equation. Since 21.5 is added to \(x\), we can isolate \(x\) by subtracting 21.5 from both sides. This gives us: \(x + 21.5 - 21.5 = -13.4 - 21.5\)
When we perform this operation, we simplify to: \(x = -34.9\)
Simplification
After isolating the variable, the next step is simplification. Simplification involves performing basic arithmetic to combine like terms and reduce the equation to its simplest form.
In the exercise, once we isolate \(x\) by subtracting 21.5 from both sides, we get: \(x = -34.9\)
This step ensures that we have a clean, simplified form of the equation where \(x\) is straightforwardly expressed. Simplification makes it easier to understand and work with the equation.
Checking the Solution
After solving for the variable, it's essential to check the solution to ensure it is correct. This verification process helps catch errors and confirm the accuracy of the result.
In the given problem, we substitute \(x = -34.9\) back into the original equation: \(x + 21.5 = -13.4\)
By substituting, we get: \(-34.9 + 21.5 = -13.4\)
Now, perform the arithmetic: \(-34.9 + 21.5 = -13.4\)
Since both sides of the equation are equal, the solution is verified and correct.
Subtraction in Equations
Subtraction is a common operation in solving equations. It is often used to move terms from one side of the equation to the other. In our example, we used subtraction to isolate the variable \(x\).
The original equation was: \(x + 21.5 = -13.4\)
To get rid of the 21.5 added to \(x\), we subtracted 21.5 from both sides: \(x + 21.5 - 21.5 = -13.4 - 21.5\)
Performing the subtraction stepwise:
  • On the left side: \(x + 21.5 - 21.5 = x\)
  • On the right side: \(-13.4 - 21.5 = -34.9\)
Thus, the use of subtraction helped us isolate the variable and find the solution to the equation.

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Most popular questions from this chapter

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