Question

Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2

Answer 1

The three equivalent equations are:

1. 2 + x = 5

2. Negative 5 + x = negative 2

3. × + (negative 4) = 7

To see why, we can solve each equation for x:
1. 2 + x = 5
Subtracting 2 from both sides:
X = 3
2. Negative 5 + x = negative 2
Adding 5 to both sides:
× = 3
3. x + (negative 4) = 7
Adding 4 to both sides:
× = 11

Therefore, equations 1, 2, and 3 are equivalent because they all have the same solution for x, which is 3. Equation 4 is not equivalent because it has a different solution for x.