We are given the equation $\frac{p}{2} = 1 - \frac{3p}{4}$ and asked to solve for $p$.

1. Problem Description

We are given the equation $\frac{p}{2} = 1 - \frac{3p}{4}$ and asked to solve for $p$.

2. Solution Steps

First, let's get rid of the fractions by multiplying both sides of the equation by the least common multiple of the denominators, which is

4. $$ 4 \cdot \frac{p}{2} = 4 \cdot (1 - \frac{3p}{4}) $$

Distribute the 4 on both sides:

$$2p = 4 - 3p$$

Now, add $3p$ to both sides of the equation to isolate $p$ on one side:

$$2p + 3p = 4 - 3p + 3p$$

$$5p = 4$$

Finally, divide both sides by 5 to solve for $p$:

$$\frac{5p}{5} = \frac{4}{5}$$

$$p = \frac{4}{5}$$

3. Final Answer

$p = \frac{4}{5}$