Mammoth Memory

Inequalities and dividing by a variable

Variable – is a symbol for a number we don’t know yet. `x` is the variable in the term `4x`.

If your equation is

`3x\ 4y<=10y` 

You cannot divide by `y`  to get `x` on its own because:

How can you divide if you don't know what `y` is?

Is it +ve value or -ve value?

Depending on whether `y`  is +ve or -ve will determine whether the inequality is flipped or not.


`3x\ 4y<=10y` 


1.  If `y=-2` then:

`3x\ 4y<=10y`

`3x\ 4(-2)\<=10(-2)`

`3x\ (-8)\<=-20`


Divide both sides by -24 and flip the inequality






2.  If `y=+2` then:

`3x\ 4y<=10y`

`3x\ (4xx2)<=10(2)`

`3x\ 8<=20`


Divide both sides by 24 but DON’T flip the inequality




The two answers give:




You can’t say which it is.

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