Drag each tile to the correct box.
Match each equation with its solution.
| Equation | Solution |
|---|---|
| [tex]n-13=-12[/tex] | |
| [tex]n+15=-10[/tex] | |
| [tex]\frac{n}{5}=-\frac{1}{5}[/tex] | |
| [tex]-5 n=1[/tex] | |
Answer (1)
Solve n − 13 = − 12 by adding 13 to both sides: n = 1 .
Solve n + 15 = − 10 by subtracting 15 from both sides: n = − 25 .
Solve 5 n = − 5 1 by multiplying both sides by 5: n = − 1 .
Solve − 5 n = 1 by dividing both sides by -5: n = − 5 1 .
Explanation
Problem Analysis We are given four equations and we need to find the solution for each one. Let's solve each equation step by step.
Solving the Equations
Solve the equation n − 13 = − 12 for n .
To isolate n , we add 13 to both sides of the equation: n − 13 + 13 = − 12 + 13 n = 1
Solve the equation n + 15 = − 10 for n .
To isolate n , we subtract 15 from both sides of the equation: n + 15 − 15 = − 10 − 15 n = − 25
Solve the equation 5 n = − 5 1 for n .
To isolate n , we multiply both sides of the equation by 5: 5 × 5 n = 5 × ( − 5 1 ) n = − 1
Solve the equation − 5 n = 1 for n .
To isolate n , we divide both sides of the equation by -5: − 5 − 5 n = − 5 1 n = − 5 1
Matching Equations with Solutions Now, we match each equation with its solution:
n − 13 = − 12 has the solution n = 1 .
n + 15 = − 10 has the solution n = − 25 .
5 n = − 5 1 has the solution n = − 1 .
− 5 n = 1 has the solution n = − 5 1 .
Final Answer The solutions to the equations are:
n − 13 = − 12 ⟹ n = 1
n + 15 = − 10 ⟹ n = − 25
5 n = − 5 1 ⟹ n = − 1
− 5 n = 1 ⟹ n = − 5 1
Examples
Understanding how to solve simple algebraic equations is crucial in many real-world scenarios. For instance, if you are managing a budget and need to determine how much you can spend each week after setting aside a certain amount for savings, you would use similar algebraic principles. Or, if you are calculating the speed required to travel a certain distance in a given time, you would also apply these concepts. Mastering these basic equations provides a foundation for more complex problem-solving in everyday life.
