Problem 103 Solve each equation. $$2.365 x... [FREE SOLUTION]

Chapter 2: Problem 103

Solve each equation. $$2.365 x+3.694=14.8095$$

Short Answer

Expert verified

x 鈮� 4.7

Step by step solution

- Isolate the variable term

First, move the constant term to the other side of the equation by subtracting 3.694 from both sides:\[ 2.365x + 3.694 - 3.694 = 14.8095 - 3.694 \]This simplifies to:\[ 2.365x = 11.1155 \]

- Solve for the variable

Next, divide both sides of the equation by 2.365 to solve for $ x $:\[ x = \frac{11.1155}{2.365} \]Carry out the division to find the value of $ x $:\[ x \approx 4.7 \]

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Key Concepts

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

Isolate the Variable

When solving a linear equation, the first step is to isolate the variable. This means you want to get the variable, often represented by letters like $x$, by itself on one side of the equation.
This way, you can easily solve for its value. In our exercise, the equation is $2.365x + 3.694 = 14.8095$.
To isolate the variable $x$, we need to move the constant (3.694) to the other side of the equation. This brings us to the next core concept: subtracting constants.

Subtracting Constants

Subtracting constants is an essential part of isolating the variable. In our equation, we have a constant term (3.694) added to $2.365x$.
To move this constant to the other side, we subtract 3.694 from both sides of the equation. This step looks like this:
\[2.365x + 3.694 - 3.694 = 14.8095 - 3.694 \]
By performing this subtraction, we get:
\[2.365x = 11.1155 \]
Now that we have isolated the variable term, we need to solve for the variable by using division.

Division to Solve Equations

After isolating the variable term, we solve for the variable by dividing both sides of the equation by the coefficient of the variable.
In our equation \[2.365x = 11.1155\], the coefficient of \x\ is 2.365. To solve for \x\, we need to divide both sides by 2.365:
\[x = \frac{11.1155}{2.365}\]
Performing the division gives us the value of \x\:
\[x \approx 4.7\]
This step allows us to find the exact numerical value of the variable.

Simplification

Simplification is about making an equation or expression as simple as possible. During the process of solving our equation, we simplified by performing operations like subtraction and division to reduce it to a form that's easy to understand and solve.
For example, we started with \[2.365x + 3.694 = 14.8095\] and simplified it step by step to eventually find \[x \approx 4.7\].
The key is to perform each arithmetic operation meticulously to maintain accuracy and simplicity in your calculations. Simplification ensures that the final answer is clear and precise.

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91影视

Solve each equation. $$2.365 x+3.694=14.8095$$

Short Answer

Step by step solution

- Isolate the variable term

- Solve for the variable

Key Concepts

Isolate the Variable

Subtracting Constants

Division to Solve Equations

Simplification

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