Question

Please help me!!! 60 points 2 questions and show work!!!!!!!!

Answer 1

2)

-12x - 0.4 > 0.2(36.5x + 80) - 55

Distributive property

-12x - 0.4 > 7.3x + 16 - 55

Combine like terms

-12x - 0.4 > 7.3x -39

Subtract both sides by 7.3x

-19.3x - 0.4 > - 39

Add 0.4 to both sides

-19.3x > -38.6

Divide both sides by -19.3 (remember when dividing a negative number, the sign will be flipped)

x < 2

1)

9/2(8 -x) + 36 = 102 - 5/2(3x+24)

Multiply both sides by 2

9(8 -x) + 72 = 204 - 5(3x+24)

Distributive propery

72 - 9x + 72 = 204 - 15x - 120

Combine like terms

- 9x + 144 = -15x + 84

Add 15x to both sides

6x + 144 = 84

Subtract 144 from both sides

6x = -60

 x = -10

Hope they help.

Answer 2

$1.\\\dfrac{9}{2}(8-x)+36=102-\dfrac{5}{2}(3x+24)\ \ \ \ |\text{multiply both sides by 2}\\\\\not2^1\cdot\dfrac{9}{\not2_1}(8-x)+2\cdot36=2\cdot102-\not2^2\cdot\dfrac{5}{\not2_1}(3x+24)\\\\9(8-x)+72=204-5(3x+24)\ \ \ \ |\text{use distributive property}\\\\(9)(8)+(9)(-x)+72=204+(-5)(3x)+(-5)(24)\\\\72-9x+72=204-15x-120\ \ \ \ |\text{use commutative and associative property}\\\\-9x+(72+72)=-15x+(204-120)\\\\-9x+144=-15x+84\ \ \ \ |\text{subtract 144 from both sides}$

$-9x=-15x-60\ \ \ \ |\text{add 15x to both sides}\\\\6x=-60\ \ \ \ |\text{divide both sides by 6}\\\\\boxed{x=-10}$

$2.\\-12x-0.4 > 0.2(36.5x+80)-55\ \ \ \ |\text{use distributive property}\\\\-12x-0.4 > (0.2)(36.5x)+(0.2)(80)-55\\\\-12x-0.4 > 7.3x+16-55\ \ \ \ |\text{use associative property}\\\\-12x-0.4 > 7.3x+(16-55)\\\\-12x-0.4 > 7.3x-39\ \ \ \ |\text{add 0.4 to both sides}\\\\-12x > 7.3x-38.6\ \ \ \ |\text{subtract 7.3x from both sides}\\\\-19.3x > -38.6\ \ \ \ \ |\text{change the signs}\\\\19.3x < 38.6\ \ \ \ |\text{divide both sides by 19.3}\\\\\boxed{x < 2}$