Solve the absolute value equation and check for extraneous solutions. 9|9-8x|=2x+3 show work

For |a|=b, solve a=b and a=-b

so

9|9-8x|=2x+3

divide both sides by 9

|9-8x|=2/9x+1/3

so

9-8x=2/9x+1/3 or 9-8x = (-2/9x+1/3)

multiply both sides by 9

81-72x=2x+3 or 81-72x=-2x-3

add 72x to both sides

81=74x+3 or 81=70x-3

for the first one, minus 3 both sides, 2nd one add 3 both sides

78=74x or 84=70x

divide both sides by 74 or 70, (first and 2nd equations respectivly)

78/74=x or 84/70=x

39/37=x or 6/5=x

if we check, they both yeild true statements

x=39/37 or 6/5