Evaluate the expression for the given value of the variable 9 | 9 -8x | = 2x + 3

Steps to solve:

9|9 - 8x| = 2x + 3

~Divide 9 to both sides

|9 - 8x| = 2/9x + 1/3

~Solve absolute value (part one)

|9 - 8x| = 2/9x + 1/3

-74/9x + 9 = 1/3 (Subtracted 2/9x to both sides)

-74/9x = -26/3 (Subtracted 9 to both sides)

x = 39/37 (Multiplied 37/39 to both sides)

~Solve absolute value (part two)

|9 - 8x| = -(2/9x + 1/3)

|9 - 8x| = -2/9x - 1/3 (Distributed negative sign to left side)

-70/9x + 9 = 11/3 (Added 2/9x to both sides)

-70/9x = -28/3 (Subtracted 9 to both sides)

x = 6/5 (Multiplied 9/-70 to both sides)

Therefore, the solutions are x = 39/37 and x = 6/5

Best of Luck!

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.

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.