Problem 28 Solve the equation. $$-4 n=-24$$... [FREE SOLUTION]

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Chapter 3: Problem 28

Solve the equation. $$-4 n=-24$$

Short Answer

Expert verified

The solution to the equation -4n = -24 is $ n = 6 $.

Step by step solution

Write down the given equation

The given linear equation is -4n = -24, which is to be solved for n.

Isolate the variable

To isolate n, divide both sides of the equation by -4. That is, n = (-24)/(-4).

Simplify the right side

Dividing -24 by -4 gives 6, hence n = 6.

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Key Concepts

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

Isolation of Variables

In algebra, the first step in solving any equation is to clearly identify the variable you need to solve for. Here, the equation is $-4n = -24$. The variable is $n$, and our goal is to 'isolate' this variable on one side of the equation. By doing this, you can figure out its exact value.
To isolate a variable, we perform operations that will "undo" anything that is currently affecting it. In our case, the $-4$ is multiplying $n$. To eliminate this operation, we will use another operation in the following step to counter it. This forms the basis of solving the equation and moving towards the solution logically.

Identify what operations are affecting the variable.
Perform operations that inverse these effects.
Ensure the operation is performed on both sides of the equation to maintain balance.

Division in Algebra

Division is one of the fundamental operations in algebra. It is often used to isolate variables, especially when they are multiplied by a number, as seen in the equation $-4n = -24$.
When you divide both sides of this equation by the same number, you are effectively balancing it, while gradually revealing the value of the variable. In our example, dividing both sides by $-4$ simplifies the expression by canceling out the $-4$ on the left. This operation possibly transforms the equation into $n = \frac{-24}{-4}$.

Division undoes multiplication, which is essential in isolating a variable.
Divide each term involved by the same number to maintain equality.

It is important to remember that dividing by a negative number changes the sign of the result, which is crucial for reaching the correct solution.

Simplification of Expressions

Once the division is performed, the resulting expression often needs simplification. Simplification involves performing any basic arithmetic operations present and tidying up the expression for clarity.
In our exercise, after dividing, we are left with the fraction $\frac{-24}{-4}$. The negative signs cancel each other out, and dividing $24$ by $4$ gives $6$. Therefore, the simplified form of the expression and the solution for the equation is $n = 6$.

This step involves checking the arithmetic calculations to ensure they are correct.
Simplifying expressions helps in understanding the equation and interpreting it correctly.

By simplifying expressions, we make the solution cleaner and much easier to read, ensuring no mistakes in interpretation.

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91影视

Solve the equation. $$-4 n=-24$$

Short Answer

Step by step solution

Write down the given equation

Isolate the variable

Simplify the right side

Key Concepts

Isolation of Variables

Division in Algebra

Simplification of Expressions

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