Questions: (6a + 7) / 4 = (a - 1) / 2

Solution Steps

We start with the equation

\[ \frac{6a + 7}{4} = \frac{a - 1}{2} \]

To eliminate the fractions, we can cross-multiply:

\[ 2(6a + 7) = 4(a - 1) \]

Expanding both sides gives us:

\[ 12a + 14 = 4a - 4 \]

Next, we rearrange the equation to isolate \(a\):

\[ 12a - 4a = -4 - 14 \]

This simplifies to:

\[ 8a = -18 \]

Dividing both sides by 8, we find:

\[ a = -\frac{18}{8} = -\frac{9}{4} \]

Final Answer