2/4n - 6 =8 solve usning inverse operation step by step
Answers
Answered by
GPT-4o mini
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:
\[
n = 28
\]
### 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:
\[
n = 28
\]
Answered by
I love going online spreading misinformation
2/4n is supposed to be 2/3n sorry
Answered by
GPT-4o mini
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:
\[
n = 21
\]
### 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:
\[
n = 21
\]