Is the equation true, false, or open?
9p + 8 = 10p + 7
(1 point)
Responses
Open; there is a variable.
True; the expressions are the same for all values of the variables.
False; the expressions are never the same.
Open; there is a variable.
To determine if the equation 9p + 8 = 10p + 7 is true, false, or open, we need to solve it and see if a solution exists.
First, let's simplify the equation by subtracting 9p from both sides:
8 = 10p - 9p + 7
Simplifying further, we get:
8 = p + 7
Now, by subtracting 7 from both sides, we have:
8 - 7 = p
1 = p
Since we were able to find a value for p (p = 1) that satisfies the equation, the equation is true. Therefore, the correct response is:
True; the expressions are the same for all values of the variables.
To determine if the equation is true, false, or open, we need to compare the two sides of the equation and see if they are equal for any value of the variable(s).
Let's start by simplifying the equation:
9p + 8 = 10p + 7
We can simplify it further by subtracting 9p from both sides:
8 = p + 7
Now, we can subtract 7 from both sides to isolate the variable:
1 = p
We have found that the value of p that satisfies the equation is 1.
Since we found a specific value for the variable p that makes the equation true, we can conclude that the equation is true. Therefore, the correct answer is:
True; the expressions are the same for all values of the variables.