Find b such that (8x+1/b)-2=x has a solution set given by {3}.
b =
To find the value of b that satisfies the equation (8x + 1/b) - 2 = x with a solution set {3}, we can start by substituting x = 3 into the equation and solve for b.
Substitute x = 3 into the equation:
(8(3) + 1/b) - 2 = 3
Simplify the equation:
24 + 1/b - 2 = 3
Combine like terms:
23 + 1/b = 3
To isolate the term with b, we can subtract 23 from both sides of the equation:
1/b = 3 - 23
1/b = -20
To solve for b, we can take the reciprocal of both sides:
b = 1/(-20)
b = -1/20
Therefore, b = -1/20 satisfies the equation (8x + 1/b) - 2 = x with a solution set {3}.