−6x + 14 < −28 or 9x + 15 ≤ −12. solve for x.

x>7 or x ≤ -3

Step-by-step explanation:

Solving the 1st inequality

-6x +14 < -28 (Collect like terms)

-6x < -28 - 14

-6x < - 42 (Divide both sides by -6)

Note: If you decide an inequality expression by a negative value, the inequality sign changes)

-6x/-6 > -42/-6

x > 7

Solving the 2nd inequality

9x + 15 ≤ −12 (Collect like terms)

9x ≤ −12 - 15

9x ≤ −27 (Divide both sides by 9)

9

9x/9 ≤ −27/9

x ≤ -3

Bring both results together, we get

x>7 or x ≤ -3

The final result is complex (i.e. can't be combined together).

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.