Solve this , idk why it’s so hard for me?

x = -10

Step-by-step explanation:

Solve for x:

(2 (6 x + 9))/3 + x = (2 (5 x - 10))/5 + 2 x

Put each term in (2 (6 x + 9))/3 + x over the common denominator 3: (2 (6 x + 9))/3 + x = (2 (6 x + 9))/3 + (3 x)/3:

(2 (6 x + 9))/3 + (3 x)/3 = (2 (5 x - 10))/5 + 2 x

(2 (6 x + 9))/3 + (3 x)/3 = (2 (6 x + 9) + 3 x)/3:

(2 (6 x + 9) + 3 x)/3 = (2 (5 x - 10))/5 + 2 x

2 (6 x + 9) = 12 x + 18:

(12 x + 18 + 3 x)/3 = (2 (5 x - 10))/5 + 2 x

Grouping like terms, 12 x + 3 x + 18 = (12 x + 3 x) + 18:

((12 x + 3 x) + 18)/3 = (2 (5 x - 10))/5 + 2 x

12 x + 3 x = 15 x:

(15 x + 18)/3 = (2 (5 x - 10))/5 + 2 x

Put each term in (2 (5 x - 10))/5 + 2 x over the common denominator 5: (2 (5 x - 10))/5 + 2 x = (2 (5 x - 10))/5 + (10 x)/5:

(15 x + 18)/3 = (2 (5 x - 10))/5 + (10 x)/5

(2 (5 x - 10))/5 + (10 x)/5 = (2 (5 x - 10) + 10 x)/5:

(15 x + 18)/3 = (2 (5 x - 10) + 10 x)/5

2 (5 x - 10) = 10 x - 20:

(15 x + 18)/3 = (10 x - 20 + 10 x)/5

10 x + 10 x = 20 x:

(15 x + 18)/3 = (20 x - 20)/5

Multiply both sides by 15:

(15 (15 x + 18))/3 = (15 (20 x - 20))/5

15/3 = (3×5)/3 = 5:

5 (15 x + 18) = (15 (20 x - 20))/5

15/5 = (5×3)/5 = 3:

5 (15 x + 18) = 3 (20 x - 20)

Expand out terms of the left hand side:

75 x + 90 = 3 (20 x - 20)

Expand out terms of the right hand side:

75 x + 90 = 60 x - 60

Subtract 60 x from both sides:

(75 x - 60 x) + 90 = (60 x - 60 x) - 60

75 x - 60 x = 15 x:

15 x + 90 = (60 x - 60 x) - 60

60 x - 60 x = 0:

15 x + 90 = -60

Subtract 90 from both sides:

15 x + (90 - 90) = -90 - 60

90 - 90 = 0:

15 x = -90 - 60

-90 - 60 = -150:

15 x = -150

Divide both sides of 15 x = -150 by 15:

(15 x)/15 = (-150)/15

15/15 = 1:

x = (-150)/15

The gcd of -150 and 15 is 15, so (-150)/15 = (15 (-10))/(15×1) = 15/15×-10 = -10:

 x = -10

hello from mrbilldoesmath!

answer:

the domain is the set { -2, 0, 2, 3}

discussion:

the domain is the set of x values in the ordered pairs (x,y). taking the x, or first component, of each ordered pair gives   -2, 0, 2, 3.

you,

mrb

, 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