Verified answer

It's just like solving an equation with one exception:

whenever you divide or multiply by a negative number you switch the sign

First:

2x-7>3

2x>10

x>5

BUT, since it's absolute value, you ALSO have to solve it for 2x-7<-3

2x-7<-3

2x<4

x<2

So, two solutions are x>5 and x<2.

The reason you have to solve it for both 2x-7>3 AND 2x-7<-3 is because of the absolute value signs. For instance:

|2(0)-7|=|0-7|=|-7|. Now, -7 is NOT bigger than 3. HOWEVER, since it is in the absolute value signs, it comes out as 7(its distance from 0) and 7 IS bigger than 3

Second:

-5<=(4-3x)/2<1

Everything you do to middle, you do to BOTH sides

-5/2<=4-3x<1/2

-5/2-4<=-3x<1-4

-6.5/-3>=x>-3/-3

2 1/6>=x>1

1)

|2x - 7| > 3

2x - 7 > 3 or 2x - 7 < -3

2x - 7 > 3

2x > 3 + 7

2x > 10

x > 10/2

x > 5

2x - 7 < -3

2x < -3 + 7

2x < 4

x < 4/2

x < 2

∴ x > 5 or x < 2

Try the other one by yourself.

you first would desire to get X by employing itself. to try this subtract the three away. So now you have 2X=-2 The to get the X thoroughly by employing itself you divide the two away (because of the fact is the guideline, to divide). So X =-a million (and that is in view which you divided the two removed from the X and on the different area it became into divided by employing the -2. desire that facilitates.