Question 986111
{{{abs(4m + 8) < 12}}}...............since {{{abs(4m + 8)=sqrt((4m + 8)^2)}}}, we will have

{{{4m + 8< 12}}} and {{{-(4m + 8)< 12}}}

solutions:

{{{4m + 8< 12}}}=>{{{4m < 12-8}}}=>{{{4m < 4}}}=>{{{highlight(m < 1)}}}
and
{{{-(4m + 8)< 12}}}=>{{{-4m - 8< 12}}}=>{{{-12 - 8< 4m}}}=>{{{-20< 4m}}}

=>{{{-20/4< m}}}=>{{{-5< m}}} or {{{highlight(m>-5)}}}

interval: {{{-5<m<1}}}

so,solution set is: {{{-4}}}, {{{-3}}},{{{-2}}},{{{-1}}},and {{{0}}}

check:
{{{m=-4}}}
{{{abs(4(-4) + 8) < 12}}}
{{{abs(-16 + 8) < 12}}}
{{{abs(-8) < 12}}}
{{{8 < 12}}}.............true

{{{m=-3}}}
{{{abs(4(-3) + 8) < 12}}}
{{{abs(-12 + 8) < 12}}}
{{{abs(-4) < 12}}}
{{{4 < 12}}}.............true

{{{m=-2}}}
{{{abs(4(-2) + 8) < 12}}}
{{{abs(-8 + 8) < 12}}}
{{{abs(0) < 12}}}
{{{0 < 12}}}.............true

{{{m=-1}}}
{{{abs(4(-1) + 8) < 12}}}
{{{abs(-4 + 8) < 12}}}
{{{abs(4) < 12}}}
{{{4 < 12}}}.............true

{{{m=0}}}
{{{abs(4(0) + 8) < 12}}}
{{{abs(0 + 8) < 12}}}
{{{abs(8) < 12}}}
{{{8 < 12}}}.............true

{{{number_line( 600, -10, 10, -5, 1 )}}}