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.
Open; there is a variable.
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 all values of the variable.
In this case, we have the equation:
9p + 8 = 10p + 7
To solve this equation, we need to isolate the variable on one side of the equation. We can do this by subtracting 10p from both sides:
9p - 10p + 8 = 10p - 10p + 7
-p + 8 = 7
Next, we can subtract 8 from both sides to further isolate the variable:
-p + 8 - 8 = 7 - 8
-p = -1
To make the variable positive, we can multiply both sides of the equation by -1:
(-1)(-p) = (-1)(-1)
p = 1
Therefore, we have found that the value of the variable p is 1.
Since there is a specific value for the variable that satisfies the equation, the equation is not open. Thus, the correct answer is: False; the expressions are never the same.
To determine whether the equation is true, false, or open, let's start by comparing the expressions on both sides of the equation.
9p + 8 = 10p + 7
By comparing the terms, we see that the variable 'p' appears on both sides of the equation. Therefore, this equation is not a true or false statement, but an open equation. It means that there are values of 'p' for which the equation is true, and there are values for which it is false.
Which value is a solution of the equation 5 – 4x = –3?
(1 point)
Responses
0
0
2
2
–3
–3
one fourth
To find the solution to the equation 5 - 4x = -3, we can isolate the variable x.
First, let's subtract 5 from both sides:
5 - 4x - 5 = -3 - 5
-4x = -8
Next, divide both sides by -4 to solve for x:
(-4x) / (-4) = (-8) / (-4)
x = 2
Therefore, the value x = 2 is a solution to the equation 5 - 4x = -3. The correct answer is: 2.
Which ordered pair is a solution of the equation y = x – 2?
(1 point)
Responses
(3, 1)
(3, 1)
(1, 3)
(1, 3)
(–1, 3)
(–1, 3)
(3, –1)
(3, –1)
To determine which ordered pair is a solution of the equation y = x - 2, we simply substitute the values of x and y into the equation and see if it holds true.
Let's check the options:
1) (3, 1):
Plugging in x = 3 and y = 1 into the equation, we have:
1 = 3 - 2
1 = 1
This equation is true for (3, 1).
2) (1, 3):
Plugging in x = 1 and y = 3 into the equation, we have:
3 = 1 - 2
3 = -1
This equation is not true for (1, 3).
3) (-1, 3):
Plugging in x = -1 and y = 3 into the equation, we have:
3 = -1 - 2
3 = -3
This equation is not true for (-1, 3).
4) (3, -1):
Plugging in x = 3 and y = -1 into the equation, we have:
-1 = 3 - 2
-1 = 1
This equation is not true for (3, -1).
From our calculations, we see that only the ordered pair (3, 1) satisfies the equation y = x - 2. Therefore, the correct answer is: (3, 1).
Which ordered pair is a solution of the equation y = 3x?
(1 point)
Responses
(–2, –9)
(–2, –9)
(–8, –18)
(–8, –18)
(–8, –3)
(–8, –3)
(–10, –30)
To determine which ordered pair is a solution of the equation y = 3x, we can substitute the values of x and y into the equation and see if it holds true.
Let's check the options:
1) (-2, -9):
Plugging in x = -2 and y = -9 into the equation, we have:
-9 = 3(-2)
-9 = -6
This equation is not true for (-2, -9).
2) (-8, -18):
Plugging in x = -8 and y = -18 into the equation, we have:
-18 = 3(-8)
-18 = -24
This equation is not true for (-8, -18).
3) (-8, -3):
Plugging in x = -8 and y = -3 into the equation, we have:
-3 = 3(-8)
-3 = -24
This equation is not true for (-8, -3).
4) (-10, -30):
Plugging in x = -10 and y = -30 into the equation, we have:
-30 = 3(-10)
-30 = -30
This equation is true for (-10, -30).
From our calculations, we see that only the ordered pair (-10, -30) satisfies the equation y = 3x. Therefore, the correct answer is: (-10, -30).
Which ordered pair is a solution of the equation y = –7x + 2?
(1 point)
Responses
(1, 2)
(1, 2)
(8, –54)
(8, –54)
(5, –35)
(5, –35)
(1, –7)