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Chapter 5: Problem 41

Solve. $$ 3.7+y=18 $$

Short Answer

Expert verified
y = 14.3

Step by step solution

01

Isolate the variable

First, we need to isolate the variable y by subtracting 3.7 from both sides of the equation. \(3.7 + y - 3.7 = 18 - 3.7\)
02

Simplify the equation

Next, simplify the left and right sides of the equation. The left side simplifies to y and the right side is calculated as follows: \(y = 18 - 3.7\)
03

Perform the subtraction

Perform the subtraction on the right side to find the value of y. \(y = 14.3\)

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Key Concepts

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

isolating variables
Isolating variables is a fundamental concept when solving linear equations. The goal is to move the variable we are solving for to one side of the equation, so it stands alone. This is done through a series of algebraic operations.
In our example, we start with the equation: \ \( 3.7 + y = 18 \ \) The variable we want to isolate is \( y \). To do this, we can use subtraction to remove the constant term (3.7) from the left side.
We subtract 3.7 from both sides of the equation: \ \( 3.7 + y - 3.7 = 18 - 3.7 \ \) This yields a simplified equation with the variable isolated: \ \( y = 18 - 3.7 \ \)
simplifying equations
Simplifying equations involves combining like terms and performing basic arithmetic operations to make the equation easier to work with. Once the variable is isolated, you will typically simplify the resulting expression to find its exact value.
In our example, after isolating the variable \( y \), we have: \ \( y = 18 - 3.7 \ \)
On the left side of the equation, \( y \) is already simplified as it stands alone. On the right side, however, we perform the subtraction to obtain a clearer and more simplified result: \ \( 18 - 3.7 = 14.3 \ \). Thus, the equation simplifies to: \ \( y = 14.3 \ \)
basic subtraction
Subtraction is one of the most basic and essential arithmetic operations. It鈥檚 simply the process of taking one number away from another.
In our problem, once we isolated \( y \), we needed to perform the subtraction on the right side to find its value. This step requires subtracting 3.7 from 18.
Here鈥檚 how you perform the subtraction: \ \( 18 - 3.7 = 14.3 \ \).
This tells us that when we subtract 3.7 from 18, we get 14.3 as the result. Thus, the solution to the equation is: \ \( y = 14.3 \ \)

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