Subtract $ \dfrac{1}{2} $ from $ t $ to get $ \dfrac{ \color{purple}{ 2t-1 } }{ 2 }$.

Step 1: Write $ t $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 2 }$.

$$ \begin{aligned} t- \frac{1}{2} & \xlongequal{\text{Step 1}} \frac{t}{\color{red}{1}} - \frac{1}{2} = \frac{ t \cdot \color{blue}{ 2 }}{ 1 \cdot \color{blue}{ 2 }} - \frac{ 1 }{ 2 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 2t } }{ 2 } - \frac{ \color{purple}{ 1 } }{ 2 }=\frac{ \color{purple}{ 2t-1 } }{ 2 } \end{aligned} $$

Multiply $2$ by $ \dfrac{2t-1}{2} $ to get $ 2t-1$.

Step 1: Write $ 2 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Cancel $ \color{blue}{ 2 } $ in first and second fraction.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} 2 \cdot \frac{2t-1}{2} & \xlongequal{\text{Step 1}} \frac{2}{\color{red}{1}} \cdot \frac{2t-1}{2} \xlongequal{\text{Step 2}} \frac{\color{blue}{1}}{1} \cdot \frac{2t-1}{\color{blue}{1}} = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 1 \cdot \left( 2t-1 \right) }{ 1 \cdot 1 } \xlongequal{\text{Step 4}} \frac{ 2t-1 }{ 1 } =2t-1 \end{aligned} $$

Combine like terms:

$$ \, \color{blue}{ \cancel{1}} \,+2t \, \color{blue}{ -\cancel{1}} \, = 2t $$

Use the distributive property.