Which of the following equations would have the solution of n=22

Question

?(1 point)
Responses

n+16=38−15
n plus 16 equals 38 minus 15

n+16=18+20
n plus 16 equals 18 plus 20

3n−28=38−14
3 n minus 28 equals 38 minus 14

n−15=7+15

Answer 1

Let's evaluate each equation to see which one yields the solution \( n = 22 \).

1. Equation: \( n + 16 = 38 - 15 \)

   Simplifying the right side: \[ n + 16 = 23 \quad (\text{since } 38 - 15 = 23) \] Now, subtract 16 from both sides: \[ n = 23 - 16 = 7 \] Not a solution.

2. Equation: \( n + 16 = 18 + 20 \)

   Simplifying the right side: \[ n + 16 = 38 \quad (\text{since } 18 + 20 = 38) \] Now, subtract 16 from both sides: \[ n = 38 - 16 = 22 \] This is a solution!

3. Equation: \( 3n - 28 = 38 - 14 \)

   Simplifying the right side: \[ 3n - 28 = 24 \quad (\text{since } 38 - 14 = 24) \] Adding 28 to both sides: \[ 3n = 24 + 28 = 52 \] Now, divide by 3: \[ n = \frac{52}{3} \approx 17.33 \] Not a solution.

4. Equation: \( n - 15 = 7 + 15 \)

   Simplifying the right side: \[ n - 15 = 22 \quad (\text{since } 7 + 15 = 22) \] Adding 15 to both sides: \[ n = 22 + 15 = 37 \] Not a solution.

Thus, the equation that has the solution \( n = 22 \) is:

\( n + 16 = 18 + 20 \).