Question 975073
9(2x – 4 ) ≥ 5 – 6x

18x-36>= 5-6x.  Distribute

24x>=41, add 6x and 36 to both sides

x>=(41/24) 

Check:  9[(82/24)- 96/24) >= 5-(246/24)
9(-14/24) >= (120/24)-(246/24)
(-126/24) >= (-126/24)

Try 0.  Should not work

9(-4) >= 5;; -36 is not >=5

Try 2.  Should work
9(0)>=5-12
0>= -7  works

Only if one divides or multiplies by a negative number does the inequality change.

On a number line, from +1.71 (with a solid dot) to the right the inequality is valid.