Is the equation true, false or open? Explain.
8+4=-5+7
show your work
The equation is true.
Work:
8 + 4 = 12
-5 + 7 = 2
So the equation can be rewritten as 12 = 2, which is not true. Therefore, the equation is false.
Alternative explanation:
8 + 4 = 12
-5 + 7 = 2
12 and 2 are not equal, so the equation is false.
Which ordered pair is a solution of the equation y=-11x+4? Make sure you show work!
(0, -7)
(-1, -7)
(1, -7)
d. (2, 26)
show your work
To determine which ordered pair is a solution to the equation y = -11x + 4, we substitute the x and y values into the equation and check if it holds true.
For option (0, -7):
y = -11x + 4
-7 = -11(0) + 4
-7 = 4
This is not true, so (0, -7) is not a solution to the equation.
For option (-1, -7):
y = -11x + 4
-7 = -11(-1) + 4
-7 = 11 + 4
-7 = 15
This is not true, so (-1, -7) is not a solution to the equation.
For option (1, -7):
y = -11x + 4
-7 = -11(1) + 4
-7 = -11 + 4
-7 = -7
This is true, so (1, -7) is a solution to the equation.
For option (2, 26):
y = -11x + 4
26 = -11(2) + 4
26 = -22 + 4
26 = -18
This is not true, so (2, 26) is not a solution to the equation.
Therefore, the ordered pair (1, -7) is the only solution to the equation y = -11x + 4.
A plumber charges $65 per hour to fix a leak. What is an equation that relates the total cost of a leak repair c to the number of hours, h, it takes the plumber to fix the leak?
show your work
The equation that relates the total cost of a leak repair c to the number of hours h can be represented as:
c = 65h
In this equation, c represents the total cost of the leak repair in dollars and h represents the number of hours it takes the plumber to fix the leak. Since the plumber charges $65 per hour, the total cost is found by multiplying the number of hours by the cost per hour, which is 65.
Solve for x:
2x=-6
show your work
To solve for x in the equation 2x = -6, you can divide both sides of the equation by 2.
2x / 2 = -6 / 2
This simplifies to:
x = -3
Therefore, x is equal to -3.
Solve for x:
x+12=-15
show your work
To solve for x in the equation x + 12 = -15, you can subtract 12 from both sides of the equation.
x + 12 - 12 = -15 - 12
This simplifies to:
x = -27
Therefore, x is equal to -27.
Solve for p:
8p – 3 = 13
show your work