Question 266654
<pre><font size = 4 color = "indigo"><b>
{{{4abs(3x-2)+6<7}}}

Isolate the absolute value

Add -6 to both sides:

{{{4abs(3x-2)<1}}}

Divide both sides by 4

{{{abs(3x-2)<1/4}}}

To remove the absolute value bars write

{{{-1/4<3x-2<1/4}}}

Multiple all three sides by 4 to clear of fractions

{{{-1<12x-8<1}}}

Add +8 to all three sides:

{{{7<12x<9}}}

Divide all three sides by 12

{{{7/12<x<9/12}}}

Reduce fractions:

{{{7/12<x<3/4}}}

Interval notation is ({{{7/12}}},{{{3/4}}})

Edwin</pre>