From the following compound inequalities, all the compound inequalities have a solution.
What is compound inequality?
A compound inequality is a type of inequality that comprises two basic inequalities.
From the given information, we have:
- 2x + 3 < 3x - 4 and 3x + 7 > 5x - 9
- 2(x -6) < 3(x+6) and 6(x+3) > 9(x-1)
- 8x + 15 ≤ 4x - 5 and -7x + 2 < -6x + 3
- -5x - 1 ≥ -7x + 9 and -4x - 7 < 5x + 11
To determine the compound inequality with no solution, we need to solve each of the inequalities.
1.
2x + 3 < 3x - 4 and 3x + 7 > 5x - 9
Collect like terms
= 2x - 3x < - 4 - 3 and 3x - 5x > - 9 - 7
= -x < -7 and -2x > -16
= x < 7 and x > 8 (has a solution)
2.
2(x -6) < 3(x+6) and 6(x+3) > 9(x-1)
Open brackets
= 2x - 12 < 3x + 18 and 6x + 18 > 9x - 9
Collect like terms
= 2x - 3x < 18 + 12 and 6x - 9x > - 9 - 18
= - x < 30 and - 3x > - 27
= x > -30 and x > 9 (has a solution)
3.
8x + 15 ≤ 4x - 5 and -7x + 2 < -6x + 3
Collect like terms
= 8x - 4x ≤ - 5 - 15 and -7x - 6x < 3 - 2
= 4x ≤ - 20 and -13x < 1
= x ≤ -5 and x < - 1/13 ( has a solution)
4.
-5x - 1 ≥ -7x + 9 and -4x - 7 < 5x + 11
= -5x + 7x ≥ 9 + 1 and -4x -5x < 11 + 7
= 2x ≥ 10 and -9x < 18
= x ≥ 5 and x < -2 ( has a solution)
Learn more about compound inequality here:
https://brainly.com/question/7070563
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