Question

How do you solve and graph `-5<3p+7<=22`?

Answer 1

`color(red)(-4 < p <= 5)`

Explanation:

Remember that you can add or subtract any amount to all components of an inequality without changing the validity or orientation of the inequality.
Therefore
`color(white)("XXX")-5 < 3p+7 < 22`
after subtracting `7` from all components
`rarrcolor(white)("XX")-12 < 3p <= 15`

Also remember that you can multiply or divide all components of an inequality by any constant greater than zero without changing the validity or orientation of the inequality.
Therefore
`color(white)("XXX")-12 < 3p <= 15`
after dividing all components by `3`
`rarrcolor(white)("XX")-4 < p <= 5`

Note that in drawing the number line graph for this solution, an open circle is used at `(-4)` to indicate that this value is not included in the solution,
and a closed (or solid) circle is used at `(+5)` to indicate that this vale is included.