Let's solve the given equation step-by-step and then check the solution.
The equation to solve is:
[tex]\[ a - \frac{1}{2} = \frac{3}{5} \][/tex]
Step 1: Isolate the variable [tex]\( a \)[/tex].
To do this, we need to add [tex]\(\frac{1}{2}\)[/tex] to both sides of the equation to get:
[tex]\[ a = \frac{3}{5} + \frac{1}{2} \][/tex]
Step 2: Find a common denominator for the fractions [tex]\(\frac{3}{5}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex].
The common denominator for 5 and 2 is 10. We will convert both fractions to have this common denominator.
Convert [tex]\(\frac{3}{5}\)[/tex] to a fraction with a denominator of 10:
[tex]\[ \frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10} \][/tex]
Convert [tex]\(\frac{1}{2}\)[/tex] to a fraction with a denominator of 10:
[tex]\[ \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10} \][/tex]
Step 3: Add the fractions.
[tex]\[ \frac{6}{10} + \frac{5}{10} = \frac{6 + 5}{10} = \frac{11}{10} \][/tex]
Step 4: Convert the improper fraction [tex]\(\frac{11}{10}\)[/tex] to a mixed number, if necessary.
[tex]\[ \frac{11}{10} = 1 \frac{1}{10} \][/tex]
So the solution to the equation is:
[tex]\[ a = 1 \frac{1}{10} \][/tex]
Step 5: Check the provided choices to find the best match.
a. [tex]\(-1 \frac{1}{10}\)[/tex]
b. [tex]\(1 \frac{1}{10}\)[/tex]
c. [tex]\(\frac{9}{16}\)[/tex]
d. [tex]\(\frac{1}{10}\)[/tex]
From the choices provided, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
