Find b such that (8x+1/b)-2=x has a solution set given by {3}.
b =
sub x = 3 into your equation
(24 + 1/b) - 2 = 3
24 + 1/b = 5
1/b = -19
b = -1/19
To find the value of b, we can substitute the given solution set {3} into the equation and solve for b.
Given equation: (8x + 1/b) - 2 = x
Substituting x = 3 into the equation: (8 * 3 + 1/b) - 2 = 3
Simplifying the equation: (24 + 1/b) - 2 = 3
Adding 2 to both sides: (24 + 1/b) = 5
Subtracting 24 from both sides: 1/b = 5 - 24
Simplifying: 1/b = -19
Taking the reciprocal of both sides: b = 1/(-19)
Therefore, the value of b is -1/19.
To find the value of b that satisfies the equation (8x + 1/b) - 2 = x with a solution set of {3}, we need to substitute the given solution, x = 3, into the equation and solve for b.
Let's start by substituting x = 3 into the equation:
(8(3) + 1/b) - 2 = 3
Now simplify this equation:
24 + 1/b - 2 = 3
Next, combine like terms:
23 + 1/b = 3
To isolate the fraction, subtract 23 from both sides:
1/b = 3 - 23
Simplifying on the right side:
1/b = -20
To solve for b, we need to take the reciprocal of both sides of the equation:
b/1 = -1/20
Thus, b = -1/20.