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# Solve the linear inequality.

0
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Solve the linear inequality.

-8<4-2x<=-5

Jun 26, 2014

#1
+576
+10

Remember how in basic algebra anything that we do to one side of an equation we do to the other as well to keep it balanced?    The same applies here with one caveat: if you multiply or divide by a negative number you must flip the inequality signs.  Here is an example of why this is important/

take 2<4, an obviously true statement and multiply both sides by -1 so we have -2<-4,  this is now not true!  If we flip the inequality so it says -2>-4 we have preserved out relation however.

Secondly, its not so much about sides in algebra as it is about hitting every "chunk" of math that is separated by a relation symbol.  With that, back to your initial question.

Let's subtract four, not from both sides, but from all three "pieces"

-12<-2x<=-9      Now we divide by -2, dont forget to flip the signs!

6>x=>9/2      And we are done!

It can also be written as  x<6 and x>=9/2

Jun 26, 2014

#1
+576
+10

Remember how in basic algebra anything that we do to one side of an equation we do to the other as well to keep it balanced?    The same applies here with one caveat: if you multiply or divide by a negative number you must flip the inequality signs.  Here is an example of why this is important/

take 2<4, an obviously true statement and multiply both sides by -1 so we have -2<-4,  this is now not true!  If we flip the inequality so it says -2>-4 we have preserved out relation however.

Secondly, its not so much about sides in algebra as it is about hitting every "chunk" of math that is separated by a relation symbol.  With that, back to your initial question.

Let's subtract four, not from both sides, but from all three "pieces"

-12<-2x<=-9      Now we divide by -2, dont forget to flip the signs!

6>x=>9/2      And we are done!

It can also be written as  x<6 and x>=9/2

jboy314 Jun 26, 2014
#2
+253
+5

I have a question. How do we get -2 when we subtract 4 from <4-2x ?

Jun 26, 2014
#3
+576
+5

When we subtracted four it killed off the 4 in the 4-2x so what is left over is just the -2x in that middle "chunk"

Jun 26, 2014
#4
+253
+5

Yes, that was the line I was speaking of. And now it all makes sense. Now I am going to try to do the next one.

Jun 26, 2014
#5
+33266
+5

Here's another inequality I want to turn into equalities.

Separately find the extreme values.

1. -8 = 4 - 2x1

Add 8 to both sides:  0 = 12 - 2x1

Add 2x1 to both sides 2x1 = 12

Divide by 2:  x1 = 6

2. 4 - 2x2 = -5

Add 5 to both sides: 9 - 2x2 = 0

Add 2x2 to both sides: 9 = 2x2

Divide by 2 to get x2 = 4.5

The extreme values are 4.5 and 6. The only point to beware of here is that x can equal the second (lower) limit, but is strictly less than the first (upper) limit. So  4.5 ≤ x < 6

Jun 26, 2014
#6
+118117
0

It is good that you asked a further question sally. We want to know that you understand (or that you do not)

Thumbs up for your clarification question.

Jun 27, 2014