Question

Which equation is true?
(12 + 17) - 9 = (23 - 7) + 4
12 + (17 - 9) = 23 - (7 + 4)
(12 + 17) - 9 = 23 - (7 + 4)
2 + (17 - 9) = 23 - (7 + 4)

Answer 1

Let's evaluate each equation one by one:

1. **Equation 1:** \( (12 + 17) - 9 = (23 - 7) + 4 \)

Left side: \( (12 + 17) - 9 = 29 - 9 = 20 \)

Right side: \( (23 - 7) + 4 = 16 + 4 = 20 \)

So, \( 20 = 20 \) is true.

2. **Equation 2:** \( 12 + (17 - 9) = 23 - (7 + 4) \)

Left side: \( 12 + (17 - 9) = 12 + 8 = 20 \)

Right side: \( 23 - (7 + 4) = 23 - 11 = 12 \)

So, \( 20 \neq 12 \) is false.

3. **Equation 3:** \( (12 + 17) - 9 = 23 - (7 + 4) \)

Left side: \( (12 + 17) - 9 = 29 - 9 = 20 \)

Right side: \( 23 - (7 + 4) = 23 - 11 = 12 \)

So, \( 20 \neq 12 \) is false.

4. **Equation 4:** \( 2 + (17 - 9) = 23 - (7 + 4) \)

Left side: \( 2 + (17 - 9) = 2 + 8 = 10 \)

Right side: \( 23 - (7 + 4) = 23 - 11 = 12 \)

So, \( 10 \neq 12 \) is false.

Based on this evaluation, the only true equation is:

**(12 + 17) - 9 = (23 - 7) + 4**.