Tryingtodowell
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for each cases how do you know which one will be negative or positiveu can consider cases as |x+1| = -(x+1) for x< -1 and |x-5| = -(x-5) for x < 5.
then from there u just solve the inequality for each case (x<-1, -1<x<5 , x > 5)
for example -1<x<5 we have:
x+1-(x-5) > 7 => -4 > 7 which isnt true so theres no value of x between -1 and 5 that satisfies the inequality
for x<-1:
-(x+1)-(x-5) > 7 => -2x-6>7 => x<1/2 but x is less than -1 so all values less than -1 are greater than 7
a similar process can be done for x>5
but I dont understand how to do itTo me graphing is easier.
Quickest way is by adding y values of both graphs by plotting points and then using those points, you can make a general graph. (this case makes it rlly easy as its an absolute value function that is translated on the y-axis).but I dont understand how to do it
Follow what i said. Draw a line and mark off -1 and 5. any number x between and including -1 and 5 will have |x+1| + |x-5| = 6 (a fixed sum - so we need at least 1 more for this sum) So x must be outside this interval; x now only needs to be more than 0.5 beyond the 2 numbers -1 and 5; i.e. at least 0.5 to the left of -1 or to the right of 5 along the (number) line.but I dont understand how to do it
uhhhTo me graphing is easier like this:
Draw the number line and mark off the 2 numbers "-1" and "5". The distance between these 2 numbers = 5-(-1) = 6. Now read the inequality this way: the distance of the number x from "-1" plus the distance of x from the number "5" is greater than 7. Now x cannot be a number within the interval: . So x must be outside this interval, to the right of 5 or to the left of -1. In fact we only need x to be greater than 0.5 (2 x 0.5 = 1 = 7 - 6)) to the right of "5" or to the left of "-1", that is
This wordy explanation may make this sound complicated. A simple diagram would show you how easy it is.
Whattt???To me graphing is easier like this:
Now x cannot be a number within the interval:
Im trying so hard to understand this but I dont get the rest of it from...To me graphing is easier like this:
Draw the number line and mark off the 2 numbers "-1" and "5". The distance between these 2 numbers = 5-(-1) = 6. Now read the inequality this way: the distance of the number x from "-1" plus the distance of x from the number "5" is greater than 7. Now x cannot be a number within the interval: . So x must be outside this interval, to the right of 5 or to the left of -1. In fact we only need x to be greater than 0.5 (2 x 0.5 = 1 = 7 - 6)) to the right of "5" or to the left of "-1", that is
This wordy explanation may make this sound complicated. A simple diagram would show you how easy it is.
I still dont get ittFollow what i said. Draw a line and mark off -1 and 5. any number x between and including -1 and 5 will have |x+1| + |x-5| = 6 (a fixed sum - so we need at least 1 more for this sum) So x must be outside this interval; x now only needs to be more than 0.5 beyond the 2 numbers -1 and 5; i.e. at least 0.5 to the left of -1 or to the right of 5 along the (number) line.
Try viewing it on desmos.I still dont get itt
Thats easy for you to say but it doesnt help when I cant do literally anything at allTry viewing it on desmos.
Just split it up into different domains and take the specific positive and negative values for that, then solve each section like a normal inequality
Say you choose any x between -1 and 5, x = 2, say. then |x+1| + |x-5| = |2+1| + |2 - 5| = 6. Choose another such number, say x = -0.7; then |x+1| + |x-5| = |-0.7 + 1| + |-0.7 -5| =0.3 + 5.7 = 6 (again). If you choose x = -3 (which is more than 0.5 to the left of -1), then |-3+1| + |-3-5| = 2 + 8 = 10 (this is greater than 7). If x = 5.2 (which is NOT more than 0.5 to the right of 5), |5.2 + 1| + |5.2-5| = 6.2 + 0.2 = 6.4 (not more than 7); so 5.2 is not a solution. You only need to look at the question geometrically; no algebra of inequalities needed.Whattt???
omgg I think I understand it now tyy
I feel bad but I still dont get yours -> like using '0.5' and stuffSay you choose any x between -1 and 5, x = 2, say. then |x+1| + |x-5| = |2+1| + |2 - 5| = 6. Choose another such number, say x = -0.7; then |x+1| + |x-5| = |-0.7 + 1| + |-0.7 -5| =0.3 + 5.7 = 6 (again). If you choose x = -3 (which is more than 0.5 to the left of -1), then |-3+1| + |-3-5| = 2 + 8 = 10 (this is greater than 7). If x = 5.2 (which is NOT more more than 0.5 to the right of 5), |5.2 + 1| + |5.2-5| = 6.2 + 0.2 = 6.4 (not more than 7); so 5.2 is not a solution. You only need to look at the question geometrically; no algebra of inequalities needed.
Note my correction to typo:
OK. Say you take x = 5.7 say. Then this number is |5.7 + 1| = 1 + 5.7 = 6.7 away from the number -1, and |5.7 -5| = 0.7 away from the number 5; so it is = the constant 6 plus 2 x 0.7 from the 2 numbers. Remember, any x outside the closed interval [-1,5] is 6 + twice its distance from the nearer of the 2 numbers -1 and 5. Remember |x+1| is |x -(-1)| and is its distance (how far away from) from the number -1, just as |x-5| is the distance of x from the number 5.I feel bad but I still dont get yours -> like using '0.5' and stuff