-6<2x-4<10 and 4<2(1-3x)<10?

Answer 1

First problem:

-6 < 2x-4 < 10
-2 < 2x < 14
-1 < x < 7
--------------------------

Second problem:

4 < 2(1-3x) < 10
4 < 2-6x < 10
2 < -6x < 8
-1/3 > x > -4/3 (reverse signs when dividing by a neg number)

Answer 2

PROBLEM 1:

-6 < 2x - 4

-2 < 2x OR 2x > -2
x > -1

2x -4 < 10
2x < 14
x < 7

Therefore, solution is -1 < x < 7

PROBLEM 2:

4< 2(1-3x)
4< 2 - 6x
6x + 4 < 2
6x < -2
x < -1/3

2(1-3x) < 10
2 -6x < 10
-6x < 8
x > -4/3 (reverse sign because you are dividing by -6, a negative number)

Therefore, solution is -4/3 < x < -1/3

Answer 3

-6<2x-4<10

we do both parts simultaneously
-6<2x-4
2x-4<10

-2<2x
2x<14

x>-1
x<7
=>x is a number in (-1,7)

we do the same for the second
4<2(1-3x)<10
this can be written in a different form (the other one could too)
2<1-3x<5

2<1-3x
1-3x<5

1<-3x
-3x<4

-1>3x
3x<-4

x>-1/3
x<-4/3

=> x is in (-4/3,-1/3)

Answer 4

-6<2x-4<10
-6+4<2x-4+4<10+4
-2<2x<14
-2/2=2x/2<14/2
-1
4<2-6x<10
4-2<2-2-6X<10-2
2<-6X< 8
-2/6>-6/-6>8/-6
-1/3>X>-8/6=-4/3

-1/3>X>-4/3

Answer 5

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