Identify if each of the following equations is TRUE, FALSE or OPEN.
3(x + 4) = 3x + 4
5x=4x
6 - (3 - 5) = - (3 - 5) + 6
The given equations are:
1. 3(x + 4) = 3x + 4
This equation is TRUE. Both sides of the equation simplify to 3x + 12.
2. 5x=4x
This equation is FALSE. If we subtract 4x from both sides, we get x = 0. However, this implies that 5(0) = 4(0), which is not true since 0 ≠ 0.
3. 6 - (3 - 5) = - (3 - 5) + 6
This equation is OPEN. We can simplify both sides to get 6 + 2 = -(-2) + 6, which further simplifies to 8 = 8. This equation is true, but since it does not involve any variables (x), it does not determine a unique solution.