Is the equation true, false, or open?
4y+8=6y+3
a. True; the expressions are the same for all values of the variables.
b. False; the expressions are never the same.
c. Open; there is a variable.***
*** - My Answer
Answer is A. True; the expression are the same for all values of the variables.
Correct, the equation 4y + 8 = 6y + 3 is an open equation because it contains a variable (y) that can take on any value. The truth value of the equation depends on the value chosen for y. To determine if the equation is true or false, we can solve it for y and see if a valid solution is obtained. By subtracting 4y from both sides of the equation and subtracting 3 from both sides, we get 8 - 3 = 6y - 4y, which simplifies to 5 = 2y. Dividing both sides by 2, we find y = 5/2.
Since the equation does have a valid solution for y (y = 5/2), we can conclude that the equation is true for that specific value of y. However, since there are infinitely many other possible values for y, the equation remains open, meaning it does not have a definite truth value for all values of y. Therefore, the correct answer is c. Open; there is a variable.