Question

1. $3(p - 4) + 12 < 4(p - 6) + 2$

Explanation:

Step1: Expand the brackets

First, we expand the left - hand side and the right - hand side of the inequality.
For the left - hand side: \(3(p - 4)+12=3p-12 + 12\)
For the right - hand side: \(4(p - 6)+2=4p-24 + 2\)

Step2: Simplify both sides

Simplify the left - hand side: \(3p-12 + 12=3p\)
Simplify the right - hand side: \(4p-24 + 2=4p-22\)
So the inequality becomes \(3p<4p - 22\)

Step3: Solve for p

Subtract \(3p\) from both sides of the inequality: \(3p-3p<4p - 3p-22\)
We get \(0 < p-22\)
Then add 22 to both sides: \(0 + 22Which gives \(22 < p\) or \(p>22\)

Answer:

The solution to the inequality \(3(p - 4)+12<4(p - 6)+2\) is \(p > 22\)