compound inequalities And Or Intersection Unio

-16 ≤ 2 + 9x ≤ 11
12 – x > 15 or 4x – 13 > 7
 

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compound inequalities And Or Intersection Unio

-16 ≤ 2 + 9x ≤ 11
 12 – x > 15 or 4x – 13 > 7

-16 ≤ 2 + 9x ≤ 11, this gives rise to two inequalities, viz.

-16 ≤ 2 + 9x         and          2 + 9x ≤ 11

rearranging both inequalities,

- 16 - 2 ≤ 9x         and          9x ≤ 11 - 2

- 18 ≤ 9x              and          9x ≤ 9

- 2 ≤ x                  and          x ≤ 1

i.e. x lies in the range defined by: - 2 ≤ x ≤ 1

 

12 – x > 15 or 4x – 13 > 7

rearranging both inequalities gives,

12 - 15 > x   or   4x > 7 + 13

-3 > x   or   4x > 20

i.e. x < -3   or   x > 5

by Level 11 User (80.9k points)

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