Question

The values of p from {1,2,3,4,5,6,7,8,9} that make 4p-p<13 true are?

Answer 1

Values that make 4p - p < 13 true are {1,2,3, and 4}, and values that make 4p - p >13 true are {5,6,7,8, and 9}.

Explanation:

Solve the first inequality.

4p - p < 13

3p < 13

p < 13/3

Any values less than 13/3.

Then solve the second inequality.

4p - p > 13

p > 13/3

Any values greater than 13/3.

Answer 2

The long way to do this is to plug each value from the list {1, 2, 3, 4, 5, 6, 7, 8, 9} into the inequality 4p-p < 13 to see which make the inequality true. Those values are then recorded for the final answer.

The shorter way is to use algebra to solve for p
4p-p < 13
3p < 13
3p/3 < 13/3
p < 4.333 which is approximate

Since we're dealing with whole numbers from the original list, we can round 4.333 up to the nearest whole number and we now have p < 5
So the solutions would be 1,2,3,4 as they all make 4p-p < 13 true
The values 5 and higher would make 4p-p too large