Question

Solve for b. Express your answer as a proper or improper fraction in simplest terms.
-1/2 - 1/2b = 1/2

Answer 1

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.