2/3(x+9) is less than or equal to 1/3(2x+12)?

Question

a x is less than or equal to 6
b x = all real numbers
c x has no solution

Answer 1

2/3(x+9)<= 1/3(2x+12)
<=> 2x +18 <= 2x +12
<=>18<=12 and that is obviously wrong for all x. So c)

Answer 2

2/3(x+9) = 2/3x + 6
1/3(2x+12) = 2/3x + 4

2/3 (x+9) is actually greater than 1/3(2x+12)

so this has no real solution

Answer 3

to compare there is a trick . lets the numeraors be the same in multiplying in the second fraction, numerator and denominator by 2

So, you have to compare 2/3(x+9) to 2/3(4x+24) or

see when 1/x+9< 1/4x+24
4x+24< x+9 x< -5
a) this is true for x lower than -5