Question

How do you solve the inequality `-c > -19`?

Answer 1

`c<19`

Explanation:

Consider the following True statement.

`-4 > -7larrcolor(blue)"TRUE"`

If we now multiply both sides of the inequality by - 1

`(-1xx-4)>(-1xx-7)`

We obtain.

`4 > 7larrcolor(red)" FALSE"`

To make the statement True, we must reverse the sign.

That is `4<7larrcolor(blue)"TRUE"`

Conclusion.

When we multiply or divide an inequality by a `color(magenta)"negative quantity"` we must `color(green)"reverse the sign of the inequality."`

`"for" -c > -19`

multiply both sides by - 1

`(-1xx-c)<(-1xx-19)larrcolor(green)" reverse sign"`

`rArrc<19" is the solution"`

Answer 2

`c < 19`

Explanation:

Given:`" "color(red)(-c > -19)`

`color(blue)("Using first principles method")`

Add `c` to both sides

`-c+c> -19+c`

`0> -19+c`

Add 19 to both sides

`0+19 > -19+19+c`

`19 > 0+c`

`19 > c larr`Observe that the 'point' of the sign is towards `c`

So `" "color(red)(c<19)`

Notice that inequality sign is now the other way round

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Using short cut method")`

Multiply both sides by (-1) and reverse the inequality sign.

`(-1)xx(-c)" " <" " (-1)xx(-19)`

`c < 19`

`color(red)("Whenever you multiply by -1 (both sides) reverse the inequality sign")`