Show all steps solve the equation check for extraneous solution 9|9-8 x|=2x+3

Answer 1

9|9-8 x|=2x+3 , x ≥ -3/2
|9-8 x|=(2x+3)/9

9-8x = (2x+3)/9
81 - 72x = 2x+3
-74x = -78
x = -78/-74
x = 39/37
or
9-8x = -(2x+3)/9
81 - 72x = -2x - 3
-70x = -84
x = 87/70 = 6/5

check:
if x = 6/5
LS = 9|9-8(6/5)|
= 27/5
RS = 2(6/5)+3
= 27/5 , so x = 6/5

if x = 39/37
LS = 9|9-8(39/37)|
= 189/37
RS = 2(39/37) + 3 = 189/37 , so x = 39/37

Answer 2

so yes?