How do you solve for "x"

Question

6 < 4x + 2≤ 10

A. 1 < x < 10/6

B. 1 < x < 2

C. 2 < x < 3

D. 3 < x < 5

Answer 1

6 < 4x + 2 ≤ 10           subtract 2 from all three arguments
4 < 4x ≤ 8                   divide all arguments by 4
1 < x ≤ 2    (note:  Answer B should have "less than or equal to")
 
p.s., I must admit to partial plagiarism of Mark M.'s answer, but now, he has partially plagiarized my answer (note: we are both somewhat fallible and we greatly enjoy correcting each other -- it makes the "Best answer" even better -- see IV&V).

Answer 2

Another way you can see this is like two equations

 

4X + 2 > 6  and   4X +2 ≤ 10

 

the first one : 4X > 6-2  =>  4X > 4  =>  X > 1

 

 

The second:  4X +2 ≤ 10  =>  4X ≤ 10-2   =>  4X ≤ 8  =>  X ≤  8/4  => X≤ 2

 

 

With the two equations you can construct  1 < X ≤  2

 

 

 

Fernando

Answer 3

6 < 4x + 2 ≤ 10           subtract 2 from all three arguments

4 < 4x ≤ 8                  divide all arguments by 4

1 < x ≤ 2                    reduce