To solve the equation [tex]\( 2a - \frac{1}{2} = 2 \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[
2a - \frac{1}{2} = 2
\][/tex]
2. To eliminate the fraction, add [tex]\(\frac{1}{2}\)[/tex] to both sides of the equation:
[tex]\[
2a - \frac{1}{2} + \frac{1}{2} = 2 + \frac{1}{2}
\][/tex]
This simplifies to:
[tex]\[
2a = 2 + \frac{1}{2}
\][/tex]
3. Convert the right-hand side to a single fraction:
[tex]\[
2 = \frac{4}{2} \quad \text{(since 2 can be expressed as } \frac{4}{2}\text{)}
\][/tex]
Therefore:
[tex]\[
2a = \frac{4}{2} + \frac{1}{2} = \frac{4 + 1}{2} = \frac{5}{2}
\][/tex]
4. Solve for [tex]\(a\)[/tex] by dividing both sides of the equation by 2:
[tex]\[
a = \frac{\frac{5}{2}}{2}
\][/tex]
To divide by 2, multiply by the reciprocal, [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
a = \frac{5}{2} \cdot \frac{1}{2} = \frac{5 \times 1}{2 \times 2} = \frac{5}{4}
\][/tex]
5. Simplify the fraction if necessary. In this case, [tex]\(\frac{5}{4}\)[/tex] is already in its simplest form.
So, the solution set is [tex]\(\left\{ \frac{5}{4} \right\}\)[/tex].
