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Chapter 2: Problem 19

Solve each equation using the Subtraction and Addition Properties of Equality. $$y-3.8=10$$

Short Answer

Expert verified
y = 13.8

Step by step solution

01

Identify the equation

The given equation is: y - 3.8 = 10
02

Isolate the variable y

To isolate y, add 3.8 to both sides of the equation. This uses the Addition Property of Equality.y - 3.8 + 3.8 = 10 + 3.8
03

Simplify both sides

Simplify the left side of the equation: y = 10 + 3.8Then, simplify the right side: y = 13.8

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Key Concepts

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

Subtraction Property of Equality
The Subtraction Property of Equality is a fundamental concept in algebra. It states that if you subtract the same number from both sides of an equation, the two sides remain equal. This property is essential when you want to isolate the variable.

For example, if you have an equation like
\( x + 5 = 12 \)
you can subtract 5 from both sides to get:
\( x + 5 - 5 = 12 - 5 \)
This simplifies to:
\( x = 7 \)
This property is very useful and straightforward. Remember, whatever you do to one side of the equation, you must do to the other to maintain balance.
Addition Property of Equality
The Addition Property of Equality is another crucial concept in algebra. It states that if you add the same number to both sides of an equation, the two sides remain equal. This property helps you when you need to isolate the variable on one side of the equation.

Consider the given exercise:
\( y - 3.8 = 10 \)
Here, to isolate y, you need to get rid of -3.8. You do this by adding 3.8 to both sides of the equation:
\( y - 3.8 + 3.8 = 10 + 3.8 \)
This simplifies to:
\( y = 13.8 \)
When using the Addition Property of Equality, always remember to perform the same operation on both sides of the equation to keep it balanced. This step is essential for solving equations accurately.
Isolate the Variable
Isolating the variable means getting the variable alone on one side of the equation. This way you can easily determine its value.

Let's go back to our example:
\( y - 3.8 = 10 \)
To isolate y, you first use the Addition Property of Equality to remove the constant term on the variable's side. We added 3.8 to both sides:
\( y - 3.8 + 3.8 = 10 + 3.8 \)
This leaves us with:
\( y = 13.8 \)
Now we have isolated y. The equation shows that the value of y is 13.8.
Isolating the variable is essential in solving algebraic equations and understanding what each variable represents. Practice isolating the variable in different types of equations to master this skill.

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