SOLUTION: Solve the compound inequality -5<4x-5<12

Question 1162680: Solve the compound inequality
-5<4x-5<12
Found 3 solutions by Theo, ikleyn, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the same principles of equalities apply to these, i.e. whatever you do to one side of he inequality, you do to the other side to maintain the inequality.
this principle is used elow.
start with -5 < 4x - 5 < 12
add 5 to each side to get 0 < 4x < 17
divide all sides by 4 to get 0 < x < 17/4
your solution is that x must be < 17/4.
you can also break this up into separate inequalities and solve each part separately.
start with -5 < 4x - 5 < 12
take -5 < 4x - 5 as the first part.
add 5 both sides to get 0 < 4x
divide both sides by 4 to get 0 < x
next work with the second part of 4x - 5 < 12
add 5 to both sides to get 4x < 17
divide both sides by 4 to get x < 17/4
from the first part you get 0 < x
from the second part you get x < 17/4
put them together and you get 0 < x < 17/4
to test, let x = 4 which is smaller than 17/4 and let x = 5 which is greater than 17/4
when x = 4, -5 < 4x - 5 < 12 becomes -5 < 11 < 12 which is true.
when x = 5, -5 < 4x - 5 < 12 bgecomes -5 < 15 < 12 which is false.
at exactly 17/4, you get -5 < 4x - 5 < 12 becomes -5 < 12 < 12 which is also false because the inequality is smaller than and not smaller than or equal.

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

On solving compound inequalities, see the lessons
    - Solving systems of linear inequalities in one unknown
    - Solving compound inequalities
in this site.

Learn the subject from there.
Consider these lessons as your handbook, textbook, guidlines, tutorials and (free of charge) home teacher.

Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Solve the compound inequality
-5<4x-5<12

- 5 < 4x - 5 < 12
- 5 + 5 < 4x - 5 + 5 < 12 + 5 ------ Adding 5 to all "sections" of compound inequality
0 < 4x < 17
------ Dividing by 4
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