ANSWER THESE SHOW YOUR WORK OR THINKING PROCESSES

To determine which equation is true when \( k = -15 \), we can substitute \( k \) into each equation and see which one is satisfied.

### Checking each equation:

#### **F: \( 3k - 11 = -34 \)**
1. Substitute \( k = -15 \):
\[
3(-15) - 11 = -34
\]
2. Calculate:
\[
-45 - 11 = -34
\]
\[
-56 \neq -34 \text{ (False)}
\]

#### **G: \( -53 + 4k = 7 \)**
1. Substitute \( k = -15 \):
\[
-53 + 4(-15) = 7
\]
2. Calculate:
\[
-53 - 60 = 7
\]
\[
-113 \neq 7 \text{ (False)}
\]

#### **H: \( \frac{k}{3} + 17 = 12 \)**
1. Substitute \( k = -15 \):
\[
\frac{-15}{3} + 17 = 12
\]
2. Calculate:
\[
-5 + 17 = 12
\]
\[
12 = 12 \text{ (True)}
\]

#### **J: \( \frac{k}{5} + 2.5 = 0.5 \)**
1. Substitute \( k = -15 \):
\[
\frac{-15}{5} + 2.5 = 0.5
\]
2. Calculate:
\[
-3 + 2.5 = 0.5
\]
\[
-0.5 \neq 0.5 \text{ (False)}
\]

### Conclusion:
The only equation that holds true when \( k = -15 \) is **H: \( \frac{k}{3} + 17 = 12 \)**.

make it shorter

Let's quickly check each equation by substituting \( k = -15 \):

### **F: \( 3k - 11 = -34 \)**
\[
3(-15) - 11 = -45 - 11 = -56 \quad (\text{False})
\]

### **G: \( -53 + 4k = 7 \)**
\[
-53 + 4(-15) = -53 - 60 = -113 \quad (\text{False})
\]

### **H: \( \frac{k}{3} + 17 = 12 \)**
\[
\frac{-15}{3} + 17 = -5 + 17 = 12 \quad (\text{True})
\]

### **J: \( \frac{k}{5} + 2.5 = 0.5 \)**
\[
\frac{-15}{5} + 2.5 = -3 + 2.5 = -0.5 \quad (\text{False})
\]

### Conclusion:
**H** is the only true equation when \( k = -15 \).