Question 249356


{{{abs(3b-2)=7}}} Start with the given equation



Break up the absolute value (remember, if you have {{{abs(x)=a}}}, then {{{x=-a}}} or {{{x=a}}})


{{{3b-2=-7}}} or {{{3b-2=7}}} Set the expression {{{3b-2}}} equal to the original value 7 and it's opposite -7





Now lets focus on the first equation  {{{3b-2=-7}}}



{{{3b=-7+2}}}Add 2 to both sides



{{{3b=-5}}} Combine like terms on the right side



{{{b=(-5)/(3)}}} Divide both sides by 3 to isolate b




{{{b=-5/3}}} Reduce





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Now lets focus on the second equation {{{3b-2=7}}}




{{{3b=7+2}}}Add 2 to both sides



{{{3b=9}}} Combine like terms on the right side



{{{b=(9)/(3)}}} Divide both sides by 3 to isolate b




{{{b=3}}} Divide






So the solutions to {{{abs(3b-2)=7}}} are:


{{{x=-5/3}}} and {{{x=3}}}




Notice if we graph  {{{y=abs(3x-2)}}} and {{{y=7}}} (just set each side equal to y and graph), we get



{{{graph(500,500,-7,5,-10,10,abs(3x-2),7)}}}  Graph of {{{y=abs(3x-2)}}} (red) and {{{y=7}}}(green)


and we can see the two graphs intersect at {{{x=-5/3}}} and {{{x=3}}}. So this verifies our answer.