Question

How do you solve `-p-4p> -10`?

Answer 1

`p\lt2`

Explanation:

equation
`-p-4p\gt-10`

concepts applied
if `-a(b)\gtc`, then `b\color(red)(\lt)c/-a`

calculation
add like terms `rArr -5p\gt-10`
divide both sides by -5 `rArr(\cancel(-5)p)/\cancel(\color(olive)(-5))\color(red)(\lt)(-10)/\color(olive)(-5)`
simplify division `rArrp\lt2`

checking
plug in any value less than 2
`-(1)-4(1)\stackrel{?}{\gt}-10`
`-1-4\stackrel{?}{\gt}-10`
`-5\gt-10`
correct!

Answer 2

`p <2`

Explanation:

You can treat an inequality in the same way as an equation, unless to multiply or divide by a negative number, in which case the inequality sign will change around.

Let's swop the negative terms onto the other sides.

`-p -4p > -10" "larr` simplify the like terms

`-5p > -10" "larr` Add 5p to both sides

`-5p +5p > -10 +5p" "larr` add 10 to both sides

`10 > 5p" "larr div 5`

`2 > p" "larr` this means the same as:

`p < 2`

Note that the same result would have been obtained by dividing by `-5` and changing the inequality sign, as explained by another contributor.

`-5p > -10`

`(-5p)/-5 < (-10)/-5" "larr` note the sign changes!

`p < 2`