Question

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

Answer 1

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