2|-x+4|>10
ive been stuck on this for a while D=
ive been stuck on this for a while D=
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alright so I'm going to rewrite this:
2|4 -x|>10 divide by 2
|4 -x|>5 Here's the tricky part, because of the absolute value, whatever is inside must be either greater than 5 so it could be 6,7,8, etc...OR it could be LESS than -5 like -6,-7,-8, etc... because the absolute value will make it positive anyway like |-82|=82>5 Because of this we break the equation into two separate ones
4 -x>5 and 4 -x<-5 then just solve both
-1>x and 9
you can plug it back into the equation to see if it makes sense, let's use -2 and 10
2|4-(-2)|>10 2|4-10|>10
2|4+2|>10 2|-6|>10
2*6>10 2(6)>10
12>10 12>10
cool they work! :)
2|4 -x|>10 divide by 2
|4 -x|>5 Here's the tricky part, because of the absolute value, whatever is inside must be either greater than 5 so it could be 6,7,8, etc...OR it could be LESS than -5 like -6,-7,-8, etc... because the absolute value will make it positive anyway like |-82|=82>5 Because of this we break the equation into two separate ones
4 -x>5 and 4 -x<-5 then just solve both
-1>x and 9
2|4-(-2)|>10 2|4-10|>10
2|4+2|>10 2|-6|>10
2*6>10 2(6)>10
12>10 12>10
cool they work! :)
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| -x+4 | > 10/2
|-x+4| > 5
evaluating the absolute value sign you will get:
-x+4 > 5 and -x+4 < -5
x<-1 and x>9
[you can check values coming from those intervals to see if it it correct]
remember an absolute value sign works like this:
|x| = +x
|-x| = +x
how I got x>9:
-x+4 < -5 [subtract 4 from both sides]
-x < -9 [multiply both sides to -1 to remove the negative signs, and by doing so the inequality sign will be reversed]
therefore, you get x > 9
|-x+4| > 5
evaluating the absolute value sign you will get:
-x+4 > 5 and -x+4 < -5
x<-1 and x>9
[you can check values coming from those intervals to see if it it correct]
remember an absolute value sign works like this:
|x| = +x
|-x| = +x
how I got x>9:
-x+4 < -5 [subtract 4 from both sides]
-x < -9 [multiply both sides to -1 to remove the negative signs, and by doing so the inequality sign will be reversed]
therefore, you get x > 9
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2|-x + 4| > 10 ==> |-x + 4| > 5.
There are two statements here.
(1) -x + 4 > 5, which gives x < -1, and
(2) -x + 4 < - 5, which gives x > 9.
The solution set in interval notation is (-∞, -1) U (9, ∞).
There are two statements here.
(1) -x + 4 > 5, which gives x < -1, and
(2) -x + 4 < - 5, which gives x > 9.
The solution set in interval notation is (-∞, -1) U (9, ∞).
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I 4 - x I > 5
5 < ( 4 - x ) < - 5
1 < - x < - 9
x < - 1 , x > 9
5 < ( 4 - x ) < - 5
1 < - x < - 9
x < - 1 , x > 9
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2|-x+4|>10
=> |-x+4|>5
=> -x+4>5 OR -x+4 < -5
=> -1>x OR +9 < x
QED
=> |-x+4|>5
=> -x+4>5 OR -x+4 < -5
=> -1>x OR +9 < x
QED