Question

How do you solve `\frac { p } { 3} + 2> \frac { p } { 2}`?

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the inequality by `color(red)(6)` to eliminate the fractions while keeping the inequality balanced. `color(red)(6)` is the Lowest Common Denominator of the two fractions:

`color(red)(6)(p/3 + 2) > color(red)(6) xx p/2`

`(color(red)(6) xx p/3) + (color(red)(6) xx 2) > cancel(color(red)(6))3 xx p/color(red)(cancel(color(black)(2)))`

`(cancel(color(red)(6))2 xx p/color(red)(cancel(color(black)(3)))) + 12 > 3p`

`2p + 12 > 3p`

Now, subtract `color(red)(2p)` from each side of the inequality to solve for `p` while keeping the inequality balanced:

`2p - color(red)(2p) + 12 > 3p - color(red)(2p)`

`0 + 12 > (3 - color(red)(2))p`

`12 > 1p`

`12 > p`

We can now reverse or "flip" the entire inequality to state the solution in terms of `p`:

`p < 12`