What is the solution of the following equation: 7n + 5 = 12?
The correct answer and explanation is:
Let’s solve the equation step-by-step:
Equation:
7n+5=127n + 5 = 12
Step 1: Isolate the term with nn
We want to get 7n7n alone on one side. To do this, subtract 5 from both sides:
7n+5−5=12−57n + 5 – 5 = 12 – 5
7n=77n = 7
Step 2: Solve for nn
Now divide both sides by 7 to solve for nn:
7n7=77\frac{7n}{7} = \frac{7}{7}
n=1n = 1
Explanation (300 words):
The equation 7n+5=127n + 5 = 12 is a simple linear equation with one variable nn. The goal is to find the value of nn that makes the equation true.
When solving linear equations, the key idea is to isolate the variable on one side. Here, the term 7n7n includes the variable multiplied by 7, and there’s a constant term +5+5 added to it. To undo the addition of 5, we perform the inverse operation, which is subtraction. Subtracting 5 from both sides keeps the equation balanced and leaves us with 7n=77n = 7.
Next, since nn is multiplied by 7, we undo this by dividing both sides of the equation by 7. This is because division is the inverse operation of multiplication. Dividing both sides by 7 gives us n=1n = 1.
This solution means that when you substitute n=1n = 1 back into the original equation, the left side equals the right side:
7(1)+5=7+5=12,7(1) + 5 = 7 + 5 = 12, which matches the right side, confirming our answer.
In summary, the solution involves applying basic algebraic principles:
- Use inverse operations to remove constants added or subtracted from the variable term.
- Use inverse operations to remove coefficients multiplying the variable.
By following these steps, you solve for the variable and find its value that satisfies the equation. Here, the solution is n=1n = 1.