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Question 63036This question is from textbook
: Solve each compound inequality and write the solution set using interval notation.
0<5-2x<=10 and -6<4-x<0
This question is from textbook
Answer by uma(370)   (Show Source):
You can put this solution on YOUR website!
given 0 < 5 - 2x < = 10
consider the first part 0 < 5 - 2x
==> 0 + 2x < 5 - 2x + 2x [adding 2x to both the sides of the equation]
==> 2x < 5
==> 2x/2 < 5/2
==> x < 5/2 --------------------(1)
Consider the second part 5 - 2x <= 10
==> 5 - 2x - 5 <= 10 - 5
==> - 2x <= 5
==> 2x >= -5 [once we changwe the sign, the inequality changes]
==> 2x/2 >= -5/2
==> x >= - 5/2 ------------------(2)
Combining (1) andd (2) the solution in interval notation would be [-5/2, 5/2)
(2) -6 < 4-x < 0
Consider the first part of the inequality -6 < 4-x
==> -6 - 4 < 4 - x - 4
==> - 10 < -x
==> 10 > x ---------------(1)
the second part, 4 - x < 0
==> 4 - x - 4 < 0 - 4
==> -x < - 4
==> x > 4 ------------------------(2)
Combining (1) andd (2) the solution in interval notation would be (4, 10)
Good Luck!!!
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