Question

Not sure how to do this. Answers are appreciated, explanations are preferred.(27, 28, and 29) :-)

Answer 1

27) 2x-1≥0 → 2x≥1 → x≥1/2 or x≥0.5


-∞------------------(-2)-------------(-1)------------0------0.5------1------------2----------+∞
×××××××××××××××××××××
this is x≥0.5

28) -4≤2x-3<4; add 3 to each part:
-4+3≤2x-3+3<4+3
-1≤2x<7. Divide all parts by 2:

-1/2≤x<7/2 OR -0.5≤x<3.5

-∞------------(-2)---------(-1)-----(-0.5)-----0--------1--------3------(3.5)-----4---------∞
××××××××××××××××××××××
This is -0.5≤x<3.5. It starts at
-0.5 and it goes until 3.49999999999
and doesn't reach 3.5

29) x/2 -x/3 >5. But x/2-x/3 = (3x-2x)/6 = x/6, then:

x/2-x/3>5 ↔ x/6>5 OR x>30

-∞-------(-30)----------(-20)-------(-10)------0--------10--------20-------30------------+∞
××××××××××
this is x>30 It starts at
30.000001
and stops +∞