Question

Solve. 4a-2≤a+1≤3a+4
4a-2-1≤a+1-1≤3a+4-1
4a-3-3≤a≤3a+3-3
4a/3-6/3≤a≤3a/3
4a/3(1/a)-2≤a≤a(1/a)
4/3-6≤a≤1
I got lost at this part. I'm not sure what to do now, if i am solving it correctly.

Solve. 3x<4-5x<5+3x
3x<4-4-5x<5-4+3x
3x/3x<-5x<1+3x/3x
I was not sure where to go from here. This is most likely incorrect, the way I am solving it.

Answer 1

4a-2 ≤ a+1 ≤ 3a+4
4a-2 ≤ a+1 AND a+1 ≤ 3a+4
3a ≤ 3 AND -2a ≤ 3
a ≤ 1 AND a ≥ -3/2

so : -3/2 ≤ a ≤ 1

3x<4-5x<5+3x
0 < 4-8x < 5
-4 < -8x < 1
1/2 > x > -1/8
or
-1/8 < x < 1/2

the reason I did not have to split up the second is that we could subtract 3x from both ends and the x's disappeared.
I had to split up the first, since I could not eliminate the x's from both ends.

Answer 2

Thank you so much.