Answered

Solve the equation. Write your answer as an integer or a simplified fraction.

[tex]\[ 2a - \frac{1}{2} = 2 \][/tex]

The solution set is [tex]\(\boxed{\ \}\)[/tex].



Answer :

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].