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.
False; the expressions are never the same.
To determine if the equation 9p + 8 = 10p + 7 is true, false, or open:
1. Start by simplifying both sides of the equation:
9p + 8 = 10p + 7
2. Combine like terms to simplify the equations:
8 = p + 7
3. Subtract 7 from both sides of the equation:
8 - 7 = p
4. Evaluate the subtraction to find:
1 = p
Since the value of p has been determined and is not an open-ended variable, we can conclude that the equation is either true or false based on the value of p.
If the value of p is equal to 1, then the equation is true:
9(1) + 8 = 10(1) + 7
9 + 8 = 10 + 7
17 = 17
If the value of p is not equal to 1, then the equation is false. For example, if we let p be any other number, say p = 2:
9(2) + 8 = 10(2) + 7
18 + 8 = 20 + 7
26 ≠ 27
Therefore, the equation 9p + 8 = 10p + 7 is generally false for values of p other than 1.
To determine whether the equation is true, false, or open, we can simplify it.
9p + 8 = 10p + 7
We can start by subtracting 9p from both sides to isolate the term with the variable:
8 = p + 7
Next, we subtract 7 from both sides:
1 = p
So, the equation is true because the value of p that satisfies the equation is p = 1.
Which value is a solution of the equation 5 – 4x = –3?
To find the solution of the equation 5 - 4x = -3, we can follow these steps:
1. Start by subtracting 5 from both sides of the equation:
5 - 5 - 4x = -3 - 5
Simplifying the left side, we get:
-4x = -8
2. Divide both sides of the equation by -4 to isolate the variable x:
-4x / -4 = -8 / -4
Simplifying, we have:
x = 2
Therefore, the value x = 2 is a solution to the equation 5 - 4x = -3.