2/4n - 6 =8 solve usning inverse operation step by step

Answer 1

To solve the equation \( \frac{2}{4}n - 6 = 8 \) using inverse operations, follow these steps:

Step 1: Simplify the equation

First, simplify \(\frac{2}{4}\) which is equivalent to \(\frac{1}{2}\). So the equation becomes:

\[ \frac{1}{2}n - 6 = 8 \]

Step 2: Isolate the term with \(n\)

Next, we want to isolate the term with \(n\) by getting rid of \(-6\). We do this by adding \(6\) to both sides of the equation:

\[ \frac{1}{2}n - 6 + 6 = 8 + 6 \]

This simplifies to:

\[ \frac{1}{2}n = 14 \]

Step 3: Eliminate the fraction

To eliminate the fraction, multiply both sides of the equation by \(2\):

\[ 2 \cdot \left(\frac{1}{2}n\right) = 2 \cdot 14 \]

This simplifies to:

\[ n = 28 \]

Step 4: Conclusion

The solution to the equation \( \frac{2}{4}n - 6 = 8 \) is:

\[ n = 28 \]

You can check your solution by substituting \(n = 28\) back into the original equation:

\[ \frac{2}{4}(28) - 6 = 8 \]

Calculating inside the parentheses:

\[ \frac{1}{2}(28) - 6 = 14 - 6 = 8 \]

Since both sides equal \(8\), the solution is verified. Thus, the final answer is:

\[ n = 28 \]

Answer 2

2/4n is supposed to be 2/3n sorry

Answer 3

No problem! Let's solve the equation \( \frac{2}{3}n - 6 = 8 \) using inverse operations, step by step.

Step 1: Isolate the term with \(n\)

The first step is to isolate the term with \(n\) by getting rid of \(-6\). To do this, add \(6\) to both sides of the equation:

\[ \frac{2}{3}n - 6 + 6 = 8 + 6 \]

This simplifies to:

\[ \frac{2}{3}n = 14 \]

Step 2: Eliminate the fraction

Next, we need to eliminate the fraction by multiplying both sides of the equation by the reciprocal of \(\frac{2}{3}\). The reciprocal of \(\frac{2}{3}\) is \(\frac{3}{2}\). Thus, we multiply both sides by \(\frac{3}{2}\):

\[ \frac{3}{2} \cdot \left(\frac{2}{3}n\right) = \frac{3}{2} \cdot 14 \]

This simplifies to:

\[ n = \frac{3 \times 14}{2} \]

Calculating the right side:

\[ n = \frac{42}{2} = 21 \]

Step 3: Conclusion

The solution to the equation \( \frac{2}{3}n - 6 = 8 \) is:

\[ n = 21 \]

Step 4: Verification

To verify the solution, substitute \(n = 21\) back into the original equation:

\[ \frac{2}{3}(21) - 6 = 8 \]

Calculating the left side:

\[ \frac{2 \times 21}{3} - 6 = \frac{42}{3} - 6 = 14 - 6 = 8 \]

Both sides equal \(8\), confirming that the solution is correct. Therefore, the final answer is:

\[ n = 21 \]