Is the equation true, false, or open? 9p + 8 = 10p + 7 (1 point) Responses Open; there is a variable. Open; there is a variable. True; the expressions are the same for all values of the variables. True; the expressions are the same for all values of the variables. False; the expressions are never the same. False; the expressions are never the same.
False; the expressions are never the same.
To determine if the equation is true, false, or open, we need to solve it.
Given equation: 9p + 8 = 10p + 7
To solve the equation, let's isolate the variable p by moving the terms involving p to one side of the equation.
Subtracting 9p from both sides:
9p + 8 - 9p = 10p + 7 - 9p
8 = p + 7
Subtracting 7 from both sides:
8 - 7 = p + 7 - 7
1 = p
So the solution to the equation is p = 1.
Since there is a single unique solution for the variable p, we can conclude that the equation is True; the expressions are the same for all values of the variables.
To determine whether the equation 9p + 8 = 10p + 7 is true, false, or open, we need to simplify and solve the equation.
First, let's combine like terms by subtracting 10p from both sides of the equation:
9p + 8 - 10p = 10p + 7 - 10p
Simplifying this, we get:
-1p + 8 = 7
Next, let's isolate the variable by subtracting 8 from both sides of the equation:
-1p + 8 - 8 = 7 - 8
Simplifying further, we have:
-1p = -1
Finally, let's solve for p by dividing both sides of the equation by -1:
-1p / -1 = -1 / -1
This gives us:
p = 1
So, the solution to the equation is p = 1.
Therefore, the equation 9p + 8 = 10p + 7 is true when p = 1.