Please solve! $$-4\left| 7-x \right|\le-20$$

Question

anonymous · Answer

move the -4 to the other side then break it into 2 equations

anonymous · Answer

hmmmm

anonymous · Answer

|7 - x| <= 5

anonymous · Answer

remove the absolute value the same way as in the last problem

anonymous · Answer

ok...

anonymous · Answer

First divide both sides by negative four. When you divide by a negative number the inequality flips. Therefore, we would end up with$$|7-x| \ge 20/4$$ Now breaking up, we get $$(7-x) \ge 20/4 ~~ and ~~ (7-x) \le 20/4$$

anonymous · Answer

so could it be $$2lex \le12$$

anonymous · Answer

Another way to write this is as $$-20/4 \le 7-x \le 20/4$$

anonymous · Answer

oh thank you guys!

anonymous · Answer

UselessMass, I have to disagree with your answer. The solution I am getting is $$(-\infty, 2] \cup [12,+\infty)$$

anonymous · Answer

hmm :D

anonymous · Answer

http://www.wolframalpha.com/input/?i=-4*abs%287-x%29+%3C%3D+-20

anonymous · Answer

You flip the inequality anytime you divide or multiply by a negative number.

anonymous · Answer

kayser, let's review. 
1) Divide by -4 and flip the inequality. $$|7-x| \ge 5$$ 2) Remove the inequality. Since this is the greater than case, we have to write two separate inequalities. $$7-x \ge 5 ~~ and ~~ 7-x \le -5$$3) Subtract 7 from both inequalities  $$-x \ge -2 ~~ and ~~ -x \le -12$$4) Divide through by -1 for both inequalities and remembering the flip the inequalities $$x \le 2 ~~ and ~~ x \ge 12$$ In set notation this becomes $$(-\infty, 2] \cup [12, +\infty)$$

anonymous · Answer

UselessMass, remember that in the case the inequality is greater than the given number, we have to write the inequality as two inequalities. It is impossible to write it as one. http://www.purplemath.com/modules/absineq.htm