Solve: [tex]$15-12 n=n+2$[/tex]
Answer (2)
Add 12 n to both sides: 15 = 13 n + 2 .
Subtract 2 from both sides: 13 = 13 n .
Divide both sides by 13: 1 = n .
The solution is 1 .
Explanation
Understanding the Problem We are given the equation 15 − 12 n = n + 2 . Our goal is to solve for n . This is a linear equation, and we will isolate n by performing algebraic manipulations on both sides of the equation.
Adding 12n to Both Sides First, we want to group the terms containing n on one side of the equation. To do this, we can add 12 n to both sides of the equation:
15 − 12 n + 12 n = n + 2 + 12 n
This simplifies to:
15 = 13 n + 2
Subtracting 2 from Both Sides Next, we want to isolate the term with n . To do this, we subtract 2 from both sides of the equation:
15 − 2 = 13 n + 2 − 2
This simplifies to:
13 = 13 n
Dividing by 13 Finally, to solve for n , we divide both sides of the equation by 13:
13 13 = 13 13 n
This simplifies to:
1 = n
Therefore, n = 1 .
Checking the Solution We can check our solution by substituting n = 1 back into the original equation:
15 − 12 ( 1 ) = 1 + 2
15 − 12 = 3
3 = 3
Since the equation holds true, our solution is correct.
Final Answer The solution to the equation 15 − 12 n = n + 2 is n = 1 .
Examples
Imagine you are balancing a budget. On one side, you have $15 and are spending $12 per item. On the other side, you start with $2 and need to buy one item. The equation helps you determine how many items you can buy so that both sides are equal. Solving such equations is crucial in managing finances, calculating costs, and making informed decisions about spending and saving.
To solve the equation 15 − 12 n = n + 2 , we add 12 n to both sides, giving us 15 = 13 n + 2 . After isolating n , we find n = 1 , and we check that this value satisfies the original equation. Therefore, the solution is n = 1 .
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