[8th grade connections academy]
is the equation true, false, or open?
4y + 8 = 6y + 3
true
false
open (my answer)
correct
Trust me:
Had it been.....
4y + 8 = 4y + 3 ---- > false , for every value of x
4y + 8 = 4y + 8 -----> true , for every value of x
4y + 8 = 6y + 3 ----> OPEN , becomes true for a certain value of x
To determine whether the equation 4y + 8 = 6y + 3 is true, false, or open, we need to solve it and see if it satisfies the given conditions.
First, let's simplify the equation by combining like terms.
4y + 8 = 6y + 3
Subtract 4y from both sides of the equation to isolate the y term.
8 = 2y + 3
Next, subtract 3 from both sides of the equation to isolate the constant term.
5 = 2y
To find the value of y, divide both sides of the equation by 2.
5/2 = y
Now, we have found the value of y, which is 5/2 or 2.5.
To check whether the equation is true, false, or open, substitute the value of y into the equation and simplify.
4(5/2) + 8 = 6(5/2) + 3
10 + 8 = 15 + 3
18 = 18
Since both sides of the equation are equal (18 = 18), the equation is true.
Therefore, the equation 4y + 8 = 6y + 3 is true.