Problem 50 Solve. If no equation is given, ... [FREE SOLUTION]

Chapter 4: Problem 50

Solve. If no equation is given, perform the indicated operation. $$ 30 n-34 n=\frac{3}{20} $$

Short Answer

Expert verified

The solution is $n = -\frac{3}{80}$.

Step by step solution

Simplify the Equation

Combine the like terms on the left side of the equation. The equation is $30n - 34n = \frac{3}{20}$. Simplify this to $-4n = \frac{3}{20}$.

Isolate the Variable

To solve for $n$, divide both sides of the equation by $-4$. This gives: $n = \frac{\frac{3}{20}}{-4}$.

Simplify the Right Side

Simplify the fraction on the right by performing the operation: $n = \frac{3}{20} \times \frac{1}{-4}$. Multiply the fractions: $n = \frac{3 \times 1}{20 \times (-4)} = \frac{3}{-80}$.

Write the Final Solution

The value of $n$ simplifies to $-\frac{3}{80}$. So, $n = -\frac{3}{80}$.

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Key Concepts

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

Simplifying Equations

Simplifying equations is like cleaning up your room to make it organized and easy to work in. When given an equation like $30n - 34n = \frac{3}{20}$, the first step is to simplify both sides as much as possible. To do this, we combine any like terms.

In this scenario, both terms $30n$ and $-34n$ involve $n$, which makes them like terms. Combining them means subtracting the coefficients:

$30 - 34 = -4$
Thus, $30n - 34n$ simplifies to $-4n$

The equation now reads $-4n = \frac{3}{20}$. This simplification makes it easier to see what our next steps are.

Combining Like Terms

Combining like terms is a fundamental skill in algebra that helps simplify expressions and equations. This process involves aggregating terms that have the same variable raised to the same power. For example, in $30n - 34n$:

- Each term has the variable $n$.- Since they share this common variable, we focus only on the numbers, or coefficients (30 and -34) associated with $n$.
Think about it like collecting apples: if you have 30 apples and take away 34 apples, you end up with $-4$ apples, or $-4n$. This step is crucial because it reduces the complexity of equations, setting the stage for solving them.

Fraction Multiplication

Fraction multiplication comes into play when solving equations that involve fractions. Once we simplified the equation to $n = \frac{\frac{3}{20}}{-4}$, we must handle the fraction multiplication necessary to arrive at the answer.

To multiply the fractions, recall that multiplying fractions is straightforward: multiply the numerators and the denominators:

$\frac{3}{20} \times \frac{1}{-4} = \frac{3 \times 1}{20 \times -4} = \frac{3}{-80}$

This approach reveals the scaled value of $n$, thus further simplifying the equation and leading us to the solution.

Isolating Variables

Isolating a variable is akin to getting it all by its lonesome on one side of the equation. In our example, once we simplified the equation to $-4n = \frac{3}{20}$, the next task was to isolate $n$.

To accomplish this, we need to perform operations that leave $n$ alone:

Divide both sides by $-4$ to isolate $n$
This involves converting the equation from $-4n = \frac{3}{20}$ to $n = \frac{\frac{3}{20}}{-4}$

This transforms the equation to a simpler fraction problem, allowing further simplification and thus determining $n$'s value effectively.

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91影视

Solve. If no equation is given, perform the indicated operation. $$ 30 n-34 n=\frac{3}{20} $$

Short Answer

Step by step solution

Simplify the Equation

Isolate the Variable

Simplify the Right Side

Write the Final Solution

Key Concepts

Simplifying Equations

Combining Like Terms

Fraction Multiplication

Isolating Variables

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