3. Write an inequality or compound inequality to describe each of the following graphs. Use the variables given. (2 points each) ​

Part 67) x > -2x>−2 and x < 3x<3

Part 68) x\leq -1x≤−1 or x\geq 1x≥1

Step-by-step explanation:

Part 67) we know that

The solution of the number line is the interval > (-2,3)

All real numbers greater than -2 and less than 3

so

The compound inequality could be

x > -2x>−2 and x < 3x<3

"And” indicates that, both statements must be true at the same time

Part 68) we know that

The solution of the number line is the interval (-∞,-1] ∪ [1,∞)

All real numbers less than or equal to -1 or all real numbers greater than or equal to 1

The compound inequality could be

x\leq -1x≤−1 or x\geq 1x≥1

"Or” indicates that, as long as either statement is true, the entire compound sentence is true

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for