solve for b. express your answer as a proper or improper fraction in simplest terms.
1/4b - 1/2 = 2/5
To solve for b, we have to isolate the variable on one side of the equation.
First, let's add 1/2 to both sides of the equation:
1/4b - 1/2 + 1/2 = 2/5 + 1/2
1/4b = 2/5 + 1/2
Next, we need to find the common denominator to add the fractions on the right side. The common denominator of 5 and 2 is 10.
2/5 can be rewritten as 4/10, so our equation becomes:
1/4b = 4/10 + 1/2
Adding the fractions:
1/4b = 4/10 + 5/10
1/4b = 9/10
To isolate b, we'll multiply both sides of the equation by 4:
4 * (1/4b) = 4 * (9/10)
1b = 36/10
Simplifying the fraction 36/10:
1b = 18/5
Therefore, b = 18/5.