Question 437310
 Start with the given inequality

{{{abs(7x-8) >-3}}}

Break up the absolute value inequality using the given rule

{{{7x-8 >-3}}} or {{{-(7x-8) >-3}}}

Now lets do the first inequality  

{{{7x-8 >-3}}}

{{{7x >-3+8}}}

{{{7x >5}}}

{{{x >5/7}}}

{{{x >0.7}}}

Now lets do the second inequality 

{{{-(7x-8) >-3}}}

{{{-7x+8 >-3}}}

{{{-7x >-3-8}}}

{{{-7x >-11}}}..........both sides multiply by {{{-1}}}

{{{7x <11}}}

{{{x <11/7}}}

{{{x <1.6}}}

So our answer is


 {{{x <1.6}}} or {{{x >0.7}}}

in interval notation

({{{-infinity}}}, {{{1.6}}}) U ({{{0.7}}},{{{infinity}}})