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.
To determine if the equation is true, false, or open, we need to simplify both sides of the equation and see if they are equal.
Given the equation: 9p + 8 = 10p + 7
First, we want to combine like terms on each side of the equation. In this case, we have 9p and 10p as the only variables, so we can add or subtract them.
9p - 10p + 8 = 7
Simplifying further, we have:
-p + 8 = 7
Next, we want to isolate the variable on one side of the equation. In this case, we can subtract 8 from both sides:
-p + 8 - 8 = 7 - 8
Simplifying further, we have:
-p = -1
Finally, we want to solve for p by dividing both sides by -1:
-p / -1 = -1 / -1
This gives us:
p = 1
Since we were able to simplify the equation and determine a specific value for p, the equation is not open.
Therefore, the answer is: False; the expressions are never the same.
To determine whether the equation is true, false, or open, we need to solve it and see if it holds true for all values of the variables involved.
Let's simplify the equation step by step:
9p + 8 = 10p + 7
First, let's isolate p on one side by subtracting 9p from both sides:
8 = 10p - 9p + 7
Simplifying:
8 = p + 7
Next, let's isolate p by subtracting 7 from both sides:
8 - 7 = p
Simplifying:
1 = p
Since we were able to find a specific value (p = 1) that satisfies the equation, the equation is not open.
Therefore, the correct answer is:
False; the expressions are never the same.