Question #13211

-16 ≤ 2 + 9x ≤ 11 12 – x > 15 or 4x – 13 > 7 I need to know how to find the solution sets written algebraically and as a union or intersection of intervals.

Expert's answer

-16 ≤ 2 + 9x ≤ 11 ==>

-18 ≤ 9x ≤ 9 ==>

-2 ≤ x ≤ 1 ==> xє[-2;1]

12 – x < 15 ==>

– x < 27 ==>

x > -27 ==> xє(-27;+∞)

4x – 13 < 7 ==>

4x < 20 ==>

x < 5 ==> xє(-∞;5)

To find the interval for x you need pay attention that 'or' statement means union of intervals and 'and' statement means intersection of intervals.

-18 ≤ 9x ≤ 9 ==>

-2 ≤ x ≤ 1 ==> xє[-2;1]

12 – x < 15 ==>

– x < 27 ==>

x > -27 ==> xє(-27;+∞)

4x – 13 < 7 ==>

4x < 20 ==>

x < 5 ==> xє(-∞;5)

To find the interval for x you need pay attention that 'or' statement means union of intervals and 'and' statement means intersection of intervals.

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