An equation is true if the expressions on either side of the equal sign are equal. An equation is false if the expressions on either side of the equal sign are not equal.An equation that contains one or more variables is called an open sentence. Is the equation 3y + 6 = 5y - 8 true, false, or open?
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1 point
True
False
open
False
To determine if the equation 3y + 6 = 5y - 8 is true, false, or open, we need to solve for the variable "y" and see if the equation holds true.
Let's solve for "y":
First, let's eliminate the variable term on one side of the equation. We can do this by subtracting 3y from both sides:
3y + 6 - 3y = 5y - 8 - 3y
This simplifies to:
6 = 2y - 8
Next, we can isolate the variable term by adding 8 to both sides:
6 + 8 = 2y - 8 + 8
This simplifies to:
14 = 2y
Finally, we can solve for "y" by dividing both sides by 2:
14/2 = 2y/2
This simplifies to:
7 = y
Now that we have found the value of "y" to be 7, we can substitute it back into the original equation and check if both sides are equal:
3(7) + 6 = 5(7) - 8
This simplifies to:
21 + 6 = 35 - 8
27 = 27
Since both sides of the equation are equal, the equation 3y + 6 = 5y - 8 is true.
To determine if the equation 3y + 6 = 5y - 8 is true, false, or open, we need to ensure that the expressions on either side of the equal sign are equal.
First, let's simplify both sides of the equation:
3y + 6 = 5y - 8
To do this, we can start by combining like terms on each side:
3y - 5y = -8 - 6
-2y = -14
Next, we can divide both sides of the equation by -2 to solve for y:
-2y / -2 = -14 / -2
y = 7
Now, substitute the value of y back into the original equation to check if it holds true:
3(7) + 6 = 5(7) - 8
21 + 6 = 35 - 8
27 = 27
Since both sides of the equation are equal (27 = 27), we can conclude that the equation 3y + 6 = 5y - 8 is true.