Drag each tile to the correct box.
Match each equation with its solution.
[tex]n=-1[/tex] [tex]n=-25[/tex] [tex]n=-\frac{1}{5}[/tex] [tex]n=1[/tex]
Equation
Solution
[tex]\frac{n}{5}=-\frac{1}{5}[/tex]
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[tex]-5 n=1[/tex]
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[tex]n+15=-10[/tex]
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[tex]n-13=-12[/tex] [ ]
Answer (2)
Solve the equation 5 n = − 5 1 by multiplying both sides by 5, which gives n = − 1 .
Solve the equation − 5 n = 1 by dividing both sides by -5, which gives n = − 5 1 .
Solve the equation n + 15 = − 10 by subtracting 15 from both sides, which gives n = − 25 .
Solve the equation n − 13 = − 12 by adding 13 to both sides, which gives n = 1 .
n = − 1 , n = − 5 1 , n = − 25 , n = 1
Explanation
Understanding the Problem We are given four equations and four possible solutions. Our goal is to match each equation with its correct solution. The equations are: 5 n = − 5 1 , − 5 n = 1 , n + 15 = − 10 , and n − 13 = − 12 . The possible solutions are: n = − 1 , n = − 25 , n = − 5 1 , and n = 1 .
Solving the First Equation Let's solve the first equation 5 n = − 5 1 for n . To do this, we multiply both sides of the equation by 5:
Multiply both sides by 5 5 n × 5 = − 5 1 × 5
Result of the First Equation n = − 1
Solving the Second Equation Now, let's solve the second equation − 5 n = 1 for n . To do this, we divide both sides of the equation by -5:
Divide both sides by -5 − 5 − 5 n = − 5 1
Result of the Second Equation n = − 5 1
Solving the Third Equation Next, let's solve the third equation n + 15 = − 10 for n . To do this, we subtract 15 from both sides of the equation:
Subtract 15 from both sides n + 15 − 15 = − 10 − 15
Result of the Third Equation n = − 25
Solving the Fourth Equation Finally, let's solve the fourth equation n − 13 = − 12 for n . To do this, we add 13 to both sides of the equation:
Add 13 to both sides n − 13 + 13 = − 12 + 13
Result of the Fourth Equation n = 1
Matching Equations to Solutions Now we can match each equation to its corresponding solution:
5 n = − 5 1 corresponds to n = − 1
− 5 n = 1 corresponds to n = − 5 1
n + 15 = − 10 corresponds to n = − 25
n − 13 = − 12 corresponds to n = 1
Examples
Understanding how to solve simple algebraic equations is crucial in many real-world scenarios. For instance, if you're trying to determine how many hours you need to work at a certain wage to earn a specific amount, you'll use equations similar to these. Imagine you need to save $100 and you earn $10 per hour. The equation would be 10 h = 100 , where h is the number of hours. Solving this gives you h = 10 , meaning you need to work 10 hours. These basic algebraic skills are fundamental for budgeting, financial planning, and problem-solving in everyday life.
The solutions match as follows: 5 n = − 5 1 gives n = − 1 ; − 5 n = 1 gives n = − 5 1 ; n + 15 = − 10 gives n = − 25 ; and n − 13 = − 12 gives n = 1 .
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