Question

Solve this please, Idk why it’s so hard for me? Thanks!!

Answer 1

Answer:

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:

Answer:  x = -10

Answer 2

I believe it is -19 not sure if that is the for sure answer