Question 150360
<pre><font size = 4 color = "indigo"><b> 

{{{(-3x-5)>=2}}}

--------------------------------------------
Learn rules for removing absolute values from
inequalities of these forms:


Rule 1:
-------------------------------------------
      
{{{abs(EXPRESSION)<N}}}, {{{abs(EXPRESSION)<=N}}} (where N is not negative)

Write as 

{{{-N < EXPRESSION < N}}}, {{{-N <= EXPRESSION <= N}}}, respectively.

then solve. [If N is negative, there is no solution,
and solution set = Ø)


------------------------------------------------------
------------------------------------------------------

Rule 2:
-------------------------------------------
{{{abs(EXPRESSION)>N}}}, {{{abs(EXPRESSION)>=N}}} (where N is not negative)

Write as 

{{{EXPRESSION < -N}}}{{{OR}}}{{{EXPRESSION > N}}}, {{{EXPRESSION <= -N}}}{{{OR}}}{{{EXPRESSION >= N}}}
respectively.

Then solve each part.  (If N is negative, solution set is 
"all real numbers".)
------------------------------------------

You need Rule 2.  I gave you Rule 1 also because you
will need it for other problems:

{{{abs(-3x-5)>=2}}}

{{{EXPRESSION = -3x-5}}}

{{{N=2}}}

So write:

{{{-3x-5 <= -2}}}{{{OR}}}{{{-3x-5 >= 2}}}

Solve each part:

Add 5 to both sides of both parts:

{{{-3x <= 3}}}{{{OR}}}{{{-3x >= 7}}}

Divide both sides of both parts by {{{-3}}},
Notice that dividing an inequality by a NEGATIVE
NUMBER reverses the inequality sign:

{{{(-3x)/(-3) >= 3/(-3)}}}{{{OR}}}{{{(-3x)/(-3) <= 7/3}}}

{{{x >= -1}}}{{{OR}}}{{{x <= -7/3}}}

So we shade the number line:

1. to the right of -1
and
2. to the left of {{{-7/3}}}, which is the same as {{{-2}}}{{{1/3}}}.


<=======@-----------@==================>
 -3       -2       -1        0        1            

The circles should be darkened since the inequalities
are all underlined:

Solution in interval notation is 

({{{-infinity}}},{{{-7/3}}}] U [{{{-1}}},{{{infinity}}})

Edwin</pre>