If a(b)=b^2 -2b and 4a(b)=a(2b)-24, what is the value of b?
1.5
4a(b) = a(2b)-24
4(b^2-2b) = (2b)^2-2(2b)-24
4b^2-8b = 4b^2-4b-24
4b = 24
b = 6
To find the value of b, we can substitute the given expressions into the equation and solve for b.
Given:
a(b) = b^2 - 2b
4a(b) = a(2b) - 24
Let's substitute the expression for a(b) into the second equation:
4(b^2 - 2b) = (2b)^2 - 2(2b) - 24
Simplifying the equation:
4b^2 - 8b = 4b^2 - 4b - 24
By subtracting 4b^2 from both sides and simplifying the equation further:
-8b = -4b - 24
Next, let's move all terms involving b to one side of the equation by adding 4b to both sides:
-8b + 4b = -4b + 4b - 24
-4b = -24
Finally, divide both sides of the equation by -4 to solve for b:
b = (-24) / (-4)
Simplifying the equation:
b = 6
Therefore, the value of b is 6.