SOLUTION: Solve the inequality. |-4x| + |-5| ≤ 1 |-4x| + -5 ≤ 1 |-4x| + ≤ 1 + 5 |-4x| ≤ 6 -6 < -4x < 6 -6/-4 > x > 6/-4 3/2 > x > -3

Algebra ->  Graphs -> SOLUTION: Solve the inequality. |-4x| + |-5| ≤ 1 |-4x| + -5 ≤ 1 |-4x| + ≤ 1 + 5 |-4x| ≤ 6 -6 < -4x < 6 -6/-4 > x > 6/-4 3/2 > x > -3      Log On


   

Question 1199369: Solve the inequality.
|-4x| + |-5| ≤ 1



|-4x| + -5 ≤ 1



|-4x| + ≤ 1 + 5


|-4x| ≤ 6


-6 < -4x < 6


-6/-4 > x > 6/-4


3/2 > x > -3/2


Let S = solution set


My answer: S = {x | 3/2 > x > -3/2}


Textbook answer: No solution.


What did I do wrong? Why is the empty set or no solution the right answer?






Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52756) About Me  (Show Source):
You can put this solution on YOUR website!
.

            You are wrong starting from the  FIRST  LINE  of your solution.

            The correct solution is as follows. 


Our starting inequality is

    |-4x| + |-5| ≤ 1.


Notice that  |-4x| = |4x|  and  |-5| = 5.  

Therefore, we can rewrite the starting inequality in this equivalent form

    |4x| + 5 <= 1

and then, subtracting 5 from both sides

    |4x| <= 1 - 5

    |4x| < -4.


But the number (absolute value) |4x| is always non-negative, so it can not be lesser than negative 4.


Hence, the original equation has no solution.


Exactly as it is stated in your textbook.

Solved and fully explained.



Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!


abs%28-4x%29%2Babs%28-5%29%3C=1

In the second absolute value expression on the left, what's inside is a constant, so...

abs%28-4x%29%2B5%3C=1

Subtract 5 from both sides....

abs%28-4x%29%3C=-4

But the absolute value expression on the left is always 0 or positive -- so there is no solution.

ANSWER: no solution