SOLUTION: Can somebody please help me out on this problem. Thanks so much! |7-2x|>13 That line is for absolute value.

Algebra ->  Expressions-with-variables -> SOLUTION: Can somebody please help me out on this problem. Thanks so much! |7-2x|>13 That line is for absolute value.       Log On


   

Question 183522: Can somebody please help me out on this problem. Thanks so much!
|7-2x|>13

That line is for absolute value.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
|7-2x|>13 

The rules for removing absolute value bars:

1. abs%28EXPRESSION%29+%3C+N

becomes:

-N+%3C+EXPRESSION+%3C+N

Same for matrix%281%2C1%2C%22%22%3C=%22%22%29

2. abs%28EXPRESSION%29+%3E+N

becomes:

matrix%281%2C3%2C+EXPRESSION%3C-N%2C++OR%2C++EXPRESSION%3EN%29

Same for matrix%281%2C1%2C%22%22%3E=%22%22%29

Yours is case 2:

abs%287-2x%29%3E13

becomes:

matrix%281%2C3%2C+7-2x%3C-13%2C++OR%2C++7-2x%3E13%29

then solve each for x

Subtract 7 from both sides

matrix%281%2C3%2C+-2x%3C-13-7%2C++OR%2C++-2x%3E13-7%29

matrix%281%2C3%2C+-2x%3C-20%2C++OR%2C++-2x%3E6%29

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

matrix%281%2C3%2C+x%3E10%2C++OR%2C++x%3C-3%29

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 



Edwin