The function w is defined by w(x)=6+3x. If 4⋅ w(z)=96, what is the value of z?
So is w(x)=w(z)?
4w(z) = 4(6+3z) = 96
24+12z = 96
12z = 72
z = 6
the x in w(x) is just a placeholder.
w(x) = 6+3x
w(z) = 6+3z
w(12)= 6+3*12
and so on.
No, in this problem, w(x) and w(z) are different functions. w(x) is defined as 6 + 3x, while w(z) is the same function but with a variable z instead of x. These two functions are equal only if x = z, but in general they are different when x and z are not equal.
No, w(x) is not equal to w(z). In the given equation, 4⋅w(z) = 96, we are looking for the value of z that satisfies this equation.
To find the value of z, we can start by substituting the expression for w(z) in the equation:
4⋅(6+3z) = 96
Next, we need to simplify the equation by distributing the 4 to each term inside the parentheses:
24 + 12z = 96
Now, we can solve for z by isolating the variable term:
12z = 96 - 24
12z = 72
Finally, divide both sides of the equation by 12 to solve for z:
z = 72 / 12
z = 6
Therefore, the value of z is 6.