Question 771585
The fact that the number is between -10 and 10 does not matter for the problem.
However, if you had to guess the number, knowing that it is between -10 and 10 would improve your chances.
 
THE GUESSER SOLUTION:
Could it be {{{0}}}?
{{{-2*0-2=0-2=-2}}} and that is not greater than 6, so {{{0}}} cannot be Jane's number.
Since {{{0}}} is  greater than -4, and it does not work, the solution must be that
Jane's number is less than -4
 
THE ALGEBRA SOLUTION:
{{{x}}}= the number Jane is thinking
{{{-2x}}}= the number Jane is thinking multiplied times {{{-2}}}
{{{-2x-2}}}= the result of multiplying Jane's number times -2, and then subtracting 2
{{{-2x-2>6}}} --> {{{-2(x+1)>6}}} (taking out the common factor {{{-2}}})
{{{-2(x+1)>6}}} --> {{{-2(x+1)/(-2)<6/(-2)}}} (because on multiplying/dividing by a negative number we are flipping around the number line, and that flips the inequality sign, see NOTE below)
{{{-2(x+1)/(-2)<6/(-2)}}}  --> {{{x+1<-3}}} (just simplifying)
{{{x+1<-3}}}  --> {{{x+1-1<-3-1}}}  --> {{{highlight(x<-4)}}} (subtracting 1 from both sides and simplifying)
So Jane's number is less than -4.
 
NOTE:
{{{number_line( 600, -10, 10, -4, -6, -8, 5 )}}} {{{-8<-6<-4<5}}}
The numbers to the left (of -4, or of any other number) are less, and the numbers to the right are more.
Multiplying times -1 means changing the signs off all the numbers, so we end up with
{{{number_line( 600, -10, 10, 4, 6, 8, -5 )}}} {{{-5<4<6<8}}} or {{{8>6>4>-5}}}
If one number was less than (to the left of) a certain number, after multiplying both numbers times -1, the order is reversed, so the signs change from < to > and from > to <.