Question

question 1 (10 points)
create your own two - step equation using
\ as the variable where the solution to the equation is n = 12
part 1: write an equation that would require two (or more) steps to solve that has a solution of n = 12.
part 2: show how you know the solution for n in your equation is equal to 12.
you can choose to either solve the equation, showing your work, or you can prove that your equation has a solution of n = 12 by substituting in 12 for n and simplifying.

Explanation:

Part 1:

Let's create the equation \( 2n + 5 = 29 \). This equation will require two steps to solve (first, subtract 5 from both sides, then divide by 2) and we'll check that \( n = 12 \) is the solution.

Part 2:

We can verify the solution by substituting \( n = 12 \) into the equation \( 2n + 5 = 29 \).

Step 1: Substitute \( n = 12 \) into the left - hand side of the equation

First, calculate \( 2n \) when \( n = 12 \). Using the formula \( 2n \), we substitute \( n = 12 \) to get \( 2\times12=24 \).

Step 2: Add 5 to the result

Then we add 5 to 24. So, \( 24 + 5=29 \).

The left - hand side of the equation \( 2n + 5 \) when \( n = 12 \) is equal to the right - hand side (29). So, \( n = 12 \) is the solution of the equation \( 2n+5 = 29 \).

Final Answers:

• Part 1: The equation is \( \boldsymbol{2n + 5=29} \)
• Part 2: By substituting \( n = 12 \) into \( 2n + 5 \), we get \( 2\times12+5=24 + 5 = 29 \), which is equal to the right - hand side of the equation \( 2n + 5 = 29 \). So \( n = 12 \) is the solution.

Answer:

Part 1:

Let's create the equation \( 2n + 5 = 29 \). This equation will require two steps to solve (first, subtract 5 from both sides, then divide by 2) and we'll check that \( n = 12 \) is the solution.

Part 2:

We can verify the solution by substituting \( n = 12 \) into the equation \( 2n + 5 = 29 \).

Step 1: Substitute \( n = 12 \) into the left - hand side of the equation

First, calculate \( 2n \) when \( n = 12 \). Using the formula \( 2n \), we substitute \( n = 12 \) to get \( 2\times12=24 \).

Step 2: Add 5 to the result

Then we add 5 to 24. So, \( 24 + 5=29 \).

The left - hand side of the equation \( 2n + 5 \) when \( n = 12 \) is equal to the right - hand side (29). So, \( n = 12 \) is the solution of the equation \( 2n+5 = 29 \).

Final Answers:

• Part 1: The equation is \( \boldsymbol{2n + 5=29} \)
• Part 2: By substituting \( n = 12 \) into \( 2n + 5 \), we get \( 2\times12+5=24 + 5 = 29 \), which is equal to the right - hand side of the equation \( 2n + 5 = 29 \). So \( n = 12 \) is the solution.