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Question 415650: could you please help me solve this problum i dont understand -11<4x-4<3 i also thought that i would let you know that there are lines underneath the < i dont know how to put them there sorry.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! < 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.
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