Final answer:
The inequality 2p - 10 > 2 + 4p, when solved for p, demonstrates that p is less than -6. This is expressed in interval notation as (-∞, -6).
Step-by-step explanation:
To solve the inequality 2p - 10 > 2 + 4p, we first need to isolate the variable p on one side. Start by subtracting 4p from both sides of the inequality:
2p - 4p - 10 > 2 - 4p + 4p
-2p - 10 > 2
Next, add 10 to both sides of the inequality to get:
-2p - 10 + 10 > 2 + 10
-2p > 12
Now, we need to divide both sides of the inequality by -2 and remember that dividing by a negative number reverses the inequality sign:
-2p / -2 < 12 / -2
p < -6
In interval notation, this is written as:
(-∞, -6)