Question 415650
< with a _ under it represents smaller than or equal.


you would show that as <=   


grateer than or equal would be shown as >=


not equal would be shown as <>


if you don't know the symbol, then just use english.


you could have said -1 smaller than or equal to 4x-4 smaller than or equal to 3 and you would have been understood.


based on what you said, I would translate this problem to read:


-11 <= 4x-4 <= 3


add 4 to all sides of this equation to get:


-7 <= 4x <= 7


divide all sides of this equation by 4 to get:


-7/4 <= x <= 7/4


that should be your answer.


as long as x is between -7/4 and 7/4, the original equation should be true.


the original equation is -11 <= 4x-4 <= 3


if you let x = -7/4, then you get:


-11 <= 4*(-7/4) - 4 <= 3


simplify to get:


-11 <= -7 - 4 <= 3


simplify further to get:


-11 <= -11 <= 3 which is true so we're good.


if you let x = 7/4, then your original equation becomes:


-11 <= (7/4)*4 - 4 <= 3


simplify to get:


-11 <= 7 - 4 <= 3


simplify further to get:


-11 <= 3 <= 3 which is true so we're still good.


if x is smaller than -7/4 or x is greater than 7/4, we will not be good.


example:


let x = -2 which is smaller than -7/4.


your original equation becomes:


-11 <= 4*(-2) - 4 <= 3


simplify to get:


-11 <= -8 - 4 <= 3


simplify further to get:


-11 <= -12 <=- 3 which is not true because -11 is not <= -12.


you can also break the problem into 2 equivalent statements.


-11 <= 4x-4 <= 3 can be broken up into the following 2 statements.


-11 <= 4x-4 and 4x-4 <= 3


you can then solve each one of them separately.


-11 <= 4x-4
add 4 to each side to get -7 <= 4x
divide each side by 4 to get -7/4 <= x


4x-4 <= 3
add 4 to each side to get 4x <= 7
divide each side by 4 to get x <= 7/4


put the 2 equations together to getr:


-7/4 <= x <= 7/4


you'll get the same answer either way.