1/b(2b-10)=17
1/b*2b=2
1/b*10=10/b
2-10/b=17
-10/b=15
The answer is -2/3
To find the value of b that satisfies the equation 1/b(2b-10) = 17, you followed the correct steps and arrived at the correct answer, which is -2/3.
Just to recap, here are the steps you took:
1. Multiply both sides of the equation by b to eliminate the denominator:
1/b * (2b - 10) = 17 * b
This simplifies to:
2b - 10 = 17b
2. Simplify the equation by combining like terms:
2b - 17b - 10 = 0
This simplifies to:
-15b - 10 = 0
3. Isolate the variable term (-15b) by adding 10 to both sides of the equation:
-15b - 10 + 10 = 0 + 10
This simplifies to:
-15b = 10
4. Solve for b by dividing both sides of the equation by -15:
-15b / -15 = 10 / -15
This simplifies to:
b = -2/3
So the solution to the equation 1/b(2b-10) = 17 is b = -2/3.