1. Is the equation true, false, or open? 5x + 2 = 6x + 11
A. Open; there is a variable.***
2. Which value is a solution of the equation 2 - 8x = -6?
A. 1***
3. Which ordered pair is a solution of the equation y = x - 4?
B. (6,2)***
4. Which ordered pair is a solution of the equation y = 4x?
B. (-1,-4)***
5. Which ordered pair is a solution of the equation y = -7x + 2?
B. (8,-54)***
6. Mike and his best friend Dan have the same birthday, but Mike is three years older than Dan.
B. (line starts at 3)***
7. -4 = g + 1
C. g = -5***
8. x - 3 = -5
x = -2***
9. 6.4 = 4x
B. 1.6***
10. -9 = r/4
D. r = -36***
11. -7 = 7/9w
C. W = -9***
12. Which equation is an identity?
C. 10p + 6 - p = 12p - 3(p-2)***
13. Which equation has no solution?
C. 4y - 5 = 4y - 6***
14. 2(h-8) - h = h -16
C. h = infinitely many solutions***
15. 3 + 6z = 13 + 6z
D. z = no solution***
16. Eric and Mark went to a ball game and visited the concession stand.
D. $3.50***
17. 6(z-2) + 4 = 10
B. z = 3***
18. 70 = -7(-2 - 2z)
A. z = 4***
19. -2x + 4 = 2(4x - 3) - 3(-8 + 4x)
A. x = 7***
20. Why don't scientists trust atoms?
Because they make up everything!
To determine whether an equation is true, false, or open, we need to simplify it and solve for the variable. Let's start by solving each equation step by step:
1. 5x + 2 = 6x + 11
To solve for x, we need to isolate the variable on one side of the equation. First, we can subtract 5x from both sides:
2 = x + 11
Next, we can subtract 11 from both sides:
-9 = x
Since we have found a specific value for x (-9), the equation is not open. It is false because it does not satisfy the original equation.
2. 2 - 8x = -6
To solve for x, we need to isolate the variable on one side of the equation. First, we can subtract 2 from both sides:
-8x = -8
Next, we can divide both sides by -8:
x = 1
The value x = 1 satisfies the equation, so it is true.
3. y = x - 4
To find a solution, we need to substitute values for x and y into the equation and see if it holds true. Let's try the first provided ordered pair (6,2):
2 = 6 - 4
2 = 2
The equation holds true for the ordered pair (6,2).
4. y = 4x
Again, we substitute the provided ordered pair (-1,-4) into the equation:
-4 = 4(-1)
-4 = -4
The equation holds true for the ordered pair (-1,-4).
5. y = -7x + 2
Substituting the provided ordered pair (8,-54) into the equation:
-54 = -7(8) + 2
-54 = -56 + 2
-54 = -54
The equation holds true for the ordered pair (8,-54).
6. The statement "Mike and his best friend Dan have the same birthday, but Mike is three years older than Dan" is not an equation.
7. -4 = g + 1
To solve for g, let's isolate the variable on one side of the equation. First, we can subtract 1 from both sides:
-5 = g
Therefore, g = -5.
8. x - 3 = -5
To solve for x, we can add 3 to both sides:
x = -2
The value x = -2 satisfies the equation.
9. 6.4 = 4x
To solve for x, we can divide both sides by 4:
1.6 = x
The value x = 1.6 satisfies the equation.
10. -9 = r/4
To solve for r, we can multiply both sides by 4:
-36 = r
The value r = -36 satisfies the equation.
11. -7 = 7/9w
To solve for w, we can multiply both sides by 9/7:
w = -9
The value w = -9 satisfies the equation.
12. "10p + 6 - p = 12p - 3(p-2)" is not an identity but an equation. To determine if it is true or false, we can simplify it and solve for p:
First, we distribute the -3 to the terms inside the parentheses:
10p + 6 - p = 12p - 3p + 6
Simplifying further:
9p + 6 = 9p + 6
Both sides of the equation are equal, so the equation is true.
13. "4y - 5 = 4y - 6" is an equation with no solution because when we simplify and solve it, we end up with contradictory statements:
4y - 5 = 4y - 6
By subtracting 4y from both sides, we have:
-5 = -6
This statement is not true, so there is no solution to the equation.
14. "2(h-8) - h = h -16" is an equation with infinitely many solutions because when we simplify and solve it, we end up with an identity where both sides are equal, regardless of the value of h:
2h - 16 - h = h - 16
Simplifying further:
h - 16 = h - 16
Both sides of the equation are equal, so any value of h would satisfy the equation, resulting in infinitely many solutions.
15. "3 + 6z = 13 + 6z" is an equation with no solution because when we simplify and solve it, we end up with contradictory statements:
3 + 6z = 13 + 6z
By subtracting 6z from both sides, we have:
3 = 13
This statement is not true, so there is no solution to the equation.
16. "Eric and Mark went to a ball game and visited the concession stand" is not an equation, but a statement. It does not have a true or false value.
17. 6(z-2) + 4 = 10
To solve for z, we can start by subtracting 4 from both sides:
6(z - 2) = 6
Then divide both sides by 6:
z - 2 = 1
Finally, add 2 to both sides:
z = 3
The value z = 3 satisfies the equation.
18. 70 = -7(-2 - 2z)
To solve for z, we can simplify the equation step by step:
-7(-2 - 2z) = 70
First, we distribute -7 to the terms inside the parentheses:
14 + 14z = 70
Then, subtract 14 from both sides:
14z = 56
To find the value of z, divide both sides by 14:
z = 4
The value z = 4 satisfies the equation.
19. -2x + 4 = 2(4x - 3) - 3(-8 + 4x)
To solve for x, let's simplify the equation step by step:
-2x + 4 = 8x - 6 - 3(-8 + 4x)
First, we distribute 2 to the terms inside the parentheses:
-2x + 4 = 8x - 6 - 24 + 12x
Next, combine like terms:
-2x + 4 = 20x - 30
To isolate the variable, subtract 20x from both sides:
-22x + 4 = -30
Then subtract 4 from both sides:
-22x = -34
Finally, divide both sides by -22:
x = 7
The value x = 7 satisfies the equation.