Question 1186195
<pre>
{{{matrix(1,3,abs(4-5x),""<="",9)}}}

Rewrite without absolute values:

{{{matrix(1,5,-9,""<="",4-5x,""<="",9)}}}

Solve for x in the middle:

Add -4 to all three sides:

{{{matrix(1,5,-9-4,""<="",4-5x-4,""<="",9-4)}}}

{{{matrix(1,5,-13,""<="",-5x,""<="",5)}}}

Divide through by -5, which reverse the inequalities:

{{{matrix(1,5,(-13)/(-5),"">="",(-5x)/(-5),"">="",(5)/(-5))}}}

{{{matrix(1,5,13/5,"">="",x,"">="",-1)}}}

Rewrite the inequality using ≤

{{{matrix(1,5,-1,""<="",x,""<="",13/5)}}}

In interval notation, that is written:

{{{matrix(1,5, "[", -1, "," , 13/5,"]")}}}

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{{{matrix(1,3,abs(3x+1),"">"",8)}}}

Rewrite without absolute values:

{{{matrix(1,9,3x+1,""<"",-8,"",OR,"",3x+1,"">"",8)}}}

Solve each part for x.  Add -1 to all sides

{{{matrix(1,9,3x+1-1,""<"",-8-1,"",OR,"",3x+1-1,"">"",8-1)}}}

{{{matrix(1,9,3x,""<"",-9,"",OR,"",3x,"">"",7)}}}

Divide all sides by 3

{{{matrix(1,9,3x/3,""<"",-9/3,"",OR,"",3x/3,"">"",7/3)}}}

{{{matrix(1,9,x,""<"",-3,"",OR,"",x,"">"",7/3)}}}

In interval notation that's:

{{{(matrix(1,3,-infinity^"",",",-3^""))}}}{{{U}}}{{{(matrix(1,3,7/3,",",infinity))}}}

Edwin</pre>