Problem 46 \(y+6=0\)... [FREE SOLUTION]

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Chapter 3: Problem 46

\(y+6=0\)

Short Answer

Expert verified

y = -6

Step by step solution

Identify the Equation

The given equation is: \( y + 6 = 0 \)

Isolate the Variable

To isolate the variable \( y \), subtract 6 from both sides of the equation: \( y + 6 - 6 = 0 - 6 \)

Simplify the Equation

Simplify the result from the previous step to find the value of \( y \): \( y = -6 \)

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Key Concepts

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

Isolate the Variable

In solving linear equations, one of the main steps is to isolate the variable. The variable is the unknown we are trying to solve for, which in this case is represented by the letter \( y \).
Our goal is to get \( y \) on one side of the equation by itself. This often involves performing operations such as addition, subtraction, multiplication, or division on both sides of the equation. Here鈥檚 a quick breakdown:

If the variable has something added to it (like in our example \( y + 6 = 0 \)), we undo this by subtracting the same number from both sides.
If the variable has something subtracted from it, we add the same number to both sides.
Similarly, we can multiply or divide both sides of the equation to get the variable alone.

Remember, whatever you do to one side of the equation, you must do to the other to maintain balance. In the exercise, we subtracted 6 from both sides: \( y + 6 - 6 = 0 - 6 \) to isolate \( y \).

Simplify the Equation

Once the variable is isolated, the next step is to simplify the equation. Simplifying means performing the arithmetic operations to combine like terms and solve for the variable.
Let's look at our exercise:

After isolating the variable \( y \) by subtracting 6, we get: \( y + 6 - 6 = 0 - 6 \).
This simplifies to: \( y = -6 \).

In this example, after performing the subtraction, there are no more operations left to perform, so \( y \) is already simplified. This step is essential because it provides the final value of the variable, revealing the solution to the equation.

Linear Equations

A linear equation is an equation involving variables to the first power, and it graphs as a straight line. The general form of a linear equation in one variable (as in our example) can be written as: \( ax + b = c \).
Let's break it down:

\( a \) represents the coefficient of the variable.
\( b \) is a constant term.
\( c \) is another constant.

In our example: \( y + 6 = 0 \).
Here, the coefficient of \( y \) is 1, \( b \) is 6, and \( c \) is 0. Linear equations are fundamental in algebra because they form the building blocks for more complex equations. Solving them involves straightforward arithmetic operations, making them a great starting point for learning how to solve equations efficiently.

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91影视

\(y+6=0\)

Short Answer

Step by step solution

Identify the Equation

Isolate the Variable

Simplify the Equation

Key Concepts

Isolate the Variable

Simplify the Equation

Linear Equations

One App. One Place for Learning.

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