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
I agree.
Of course, the mere presence of a variable does not mean it's open.
2y+3 = 2y+3 is true for any y
2y+3 = 2y+2 is false for any y
Your answer is correct. The equation is open because it contains a variable.
To determine if the equation 4y + 8 = 6y + 3 is true, false, or open, we need to compare the two expressions on each side of the equation.
First, we can simplify both sides of the equation by combining like terms. On the left side, 4y and 6y are like terms, so we can combine them to get 10y. On the right side, there are no like terms, so the expression remains the same. We have:
10y + 8 = 6y + 3
Next, we want to isolate the variable, y, on one side of the equation. We can do this by subtracting 6y from both sides:
10y - 6y + 8 = 6y - 6y + 3
This simplifies to:
4y + 8 = 3
Now, we can further isolate the variable by subtracting 8 from both sides:
4y + 8 - 8 = 3 - 8
Which simplifies to:
4y = -5
Finally, we divide both sides of the equation by 4 to solve for y:
(4y) / 4 = (-5) / 4
This gives us:
y = -5/4
Since we were able to solve for y and obtain a specific value, -5/4, the equation is not open. Therefore, the correct answer is:
b. False; the expressions are never the same.