Solve (x - 2 < 5) u (x + 7 > 6).

a) {x | -1 < x < 7}
b) {all real numbers}
c) ø

A) {x | -1 < x < 7}

Step-by-step explanation:

Given in the question two inequalities,

Inequality 1

(x - 2 < 5)

 x < 5 + 2

 x < 7

x is smaller than 7

Inequality 2

(x + 7 > 6)

 x > 6 - 7

 x > -1

x is greater then -1

When (x - 2 < 5) U (x + 7 > 6).

              (x < 7)   U  (x > -1)    

                    -1 <  x  < 7

When combined, x is greater than -1 but smaller than 7

, 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

5x + 5

step-by-step explanation:

you should always add the diagrams and graphs we cannot see. this particular question is kind of borderline because we can make a graph for you.

(f + g)x = -x^2 +3x + 5 + x^2 + 2x

(f + g)x = 5x + 5

the graph of z = 5x + 5 is shown below. always use desmos when in doubt.