Solve for b. Express your answer as a proper or improper fraction in simplest terms.
-1/2 - 1/2b = 1/2
To solve for b, we need to isolate the variable on one side of the equation.
First, let's simplify the equation by finding a common denominator for the fractions on the left side:
-1/2 - 1/2b = 1/2
The common denominator for 1/2 and 1/2b is 2b, so let's rewrite the equation with the common denominator:
-1/2 - (1/2)*(1/b) = 1/2
Next, let's combine the fractions on the left side:
-1/2 - 1/2b = 1/2
Multiply the second fraction on the left side by 1/b:
-1/2 - (1*1)/(2*b) = 1/2
Simplify the numerator of the second fraction:
-1/2 - 1/(2b) = 1/2
The denominators of both fractions on the left side are the same, so we can combine them:
(-1 - 1)/(2b) = 1/2
Simplify the numerator:
-2/(2b) = 1/2
Simplify the left side by canceling out the common factor of 2:
-1/b = 1/2
To isolate b, we can multiply both sides of the equation by -1:
(-1/b)(-1) = (1/2)(-1)
The -1's cancel on the left side:
1/b = -1/2
To solve for b, take the reciprocal of both sides of the equation:
b/1 = -2/1
Simplifying, we get:
b = -2
So the solution is b = -2.