if a and b are integers, which equation is always true

1 a/b= b/a
2 a-b= b-a
3 a+2b= b+2a
4 a+b=b+a

4, because if a is 3 and b is 5, 1) 3/5=.6, but 5/3=1.66, 2) 3-5=-2, 5-3=2, 3) 3+(10)=13, 5+(6)=11, 4) 3+5=8, 5+3=8

Well, let me put on my jester hat and answer your question with some humor!

Out of the given equations, the one that is always true, no matter what, is option 4: a+b=b+a.

Why, you ask? Well, it's like saying if you have a slice of delicious pizza and a friend also has a slice of the same tasty pizza, no matter who you ask first, the result will always be the same – you both have pizza!

In mathematical terms, this equation is following the lovely commutative property, where addition doesn't really care about the order of the numbers involved. So, go ahead and have some fun with those integers – just remember that math and pizza go great together, but not as toppings!

To determine which equation is always true for any values of integers a and b, we can analyze each equation one by one.

1. a/b = b/a
To check if this equation is always true, we can perform a simple test by assigning integer values to a and b. Let's say a = 2 and b = 4. Substituting these values into the equation:
2/4 = 4/2
0.5 = 2

Since the equality does not hold, the equation a/b = b/a is not always true.

2. a - b = b - a
Again, let's assign values to a and b. Let a = 3 and b = 5, then substitute them into the equation:
3 - 5 = 5 - 3
-2 = 2

Since the equality does not hold, the equation a - b = b - a is not always true.

3. a + 2b = b + 2a
Let's perform the same test. Assume a = 4 and b = 2:
4 + 2(2) = 2 + 2(4)
4 + 4 = 2 + 8
8 = 10

Again, the equality does not hold, making a + 2b = b + 2a not always true.

4. a + b = b + a
Now, we will test the last equation. Let a = 5 and b = 6:
5 + 6 = 6 + 5
11 = 11

In this case, the equality holds true for any values of integers a and b. Therefore, the equation a + b = b + a is always true for all integers.

In conclusion, out of the given equations, the equation a + b = b + a (option 4) is the one that is always true for any integer values of a and b.

My response is my family

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