Question: User: 8p+6>30-2p find the lowest interger value of p given
1. **State the problem:** We need to find the lowest integer value of $p$ such that the inequality $8p + 6 > 30 - 2p$ holds.
2. **Write the inequality:**
$$8p + 6 > 30 - 2p$$
3. **Add $2p$ to both sides to get all $p$ terms on one side:**
$$8p + 2p + 6 > 30 - \cancel{2p} + \cancel{2p}$$
$$10p + 6 > 30$$
4. **Subtract 6 from both sides:**
$$10p + 6 - 6 > 30 - 6$$
$$10p > 24$$
5. **Divide both sides by 10:**
$$\frac{10p}{10} > \frac{24}{10}$$
$$p > 2.4$$
6. **Interpret the inequality:** Since $p$ must be greater than $2.4$, the lowest integer value satisfying this is $p = 3$.
**Final answer:** The lowest integer value of $p$ is **3**.