Question 183522
|7-2x|>13 

<pre><font size = 4 color = "indigo"><b>
The rules for removing absolute value bars:

1. {{{abs(EXPRESSION) < N}}}

becomes:

{{{-N < EXPRESSION < N}}}

Same for {{{matrix(1,1,""<="")}}}

2. {{{abs(EXPRESSION) > N}}}

becomes:

{{{matrix(1,3, EXPRESSION<-N,  OR,  EXPRESSION>N)}}}

Same for {{{matrix(1,1,"">="")}}}

Yours is case 2:

{{{abs(7-2x)>13}}}

becomes:

{{{matrix(1,3, 7-2x<-13,  OR,  7-2x>13)}}}

then solve each for x

Subtract 7 from both sides

{{{matrix(1,3, -2x<-13-7,  OR,  -2x>13-7)}}}

{{{matrix(1,3, -2x<-20,  OR,  -2x>6)}}}

Divide through by -2, remembering that when we
divide both sides of an inequality by a negative
number, the inequality symbols reverse directions:

{{{matrix(1,3, x>10,  OR,  x<-3)}}}

Then we place this on a number line:

<=============o--------------------------------------o============>
 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 

In interval notation this is 

{{{matrix(1,11, "(",-infinity, ",", -3,")", U, "(",10,",",infinity,")")}}}

Edwin</pre>