Question

Select all of the equations below that are equivalent to: p − q = 12

p - q + 4 = 16
3 + p - q = 17
p - q + 7 = 17
5 + p - q = 16

Answer 1

To determine which equations are equivalent to \( p - q = 12 \), we will manipulate each equation to see if we can simplify it to \( p - q = 12 \).

1. **Equation:** \( p - q + 4 = 16 \)
**Manipulation:**
\( p - q = 16 - 4 \)
\( p - q = 12 \)
**Equivalent:** Yes

2. **Equation:** \( 3 + p - q = 17 \)
**Manipulation:**
\( p - q = 17 - 3 \)
\( p - q = 14 \)
**Equivalent:** No

3. **Equation:** \( p - q + 7 = 17 \)
**Manipulation:**
\( p - q = 17 - 7 \)
\( p - q = 10 \)
**Equivalent:** No

4. **Equation:** \( 5 + p - q = 16 \)
**Manipulation:**
\( p - q = 16 - 5 \)
\( p - q = 11 \)
**Equivalent:** No

Thus, the only equivalent equation to \( p - q = 12 \) is:

**Answer:** \( p - q + 4 = 16 \)