If v,w,x,y, and z are consecutive multiples of 3, counting from smallest to largest. What is the value of v-w-x+y in terms of z?
A.4z-4
B.-12
C.-30
D.0
E.4z
v-w = -3
-x+y = 3
adding them up gives 0
To find the value of v - w - x + y in terms of z, we need to express all these variables in terms of z.
Given that v, w, x, y, and z are consecutive multiples of 3, counting from smallest to largest, we can represent them as follows:
v = 3z
w = 6z
x = 9z
y = 12z
Now, let's substitute these expressions into v - w - x + y:
v - w - x + y = (3z) - (6z) - (9z) + (12z)
Simplifying the expression, we get:
v - w - x + y = -12z + 12z
The terms -12z and 12z cancel each other out, resulting in:
v - w - x + y = 0
Therefore, the value of v - w - x + y in terms of z is 0, which corresponds to option D.
To find the value of v-w-x+y in terms of z, we need to determine the relationship between the values v, w, x, y, and z.
We are given that v, w, x, y, and z are consecutive multiples of 3, counting from smallest to largest. This means that the values share a common difference of 3.
Let's express the values in terms of the first number (smallest multiple of 3), which we'll call v.
v = v
w = v + 3
x = v + 6
y = v + 9
z = v + 12
Now, substitute these values into the expression v - w - x + y:
v - w - x + y = v - (v + 3) - (v + 6) + (v + 9)
= v - v - 3 - v - 6 + v + 9
= -3 - 6 + 9
= 0
Therefore, the value of v - w - x + y in terms of z is 0.
The correct answer is D. 0.