2HGO(s) + 43.4 kcal -> 2Hg(I) + O2(g)

x = -9, 0 = -1, x \ne 0

Explanation:

[-54/x = 6  0x = 9]

Isolate x for - 54/x = 6 : x = -9

-54/x = 6

Multiply both sides by x

-54/x = 6x

Simplify - 54/x x :  -54

-54x x = 6x

Multiply fractions: a . b/c = a . b/c

= -54x/x

Cancel the common factor: x

= -54

- 54 = 6x

Switch sides

6x = -54

Divide both sides by 6

6x/6 = -54/6

Simplify

6x/6 = -54/6

Simplify 6x/6:  -9

6x/6

Divide the numbers: 6/6 = 1

= x

Simplify

-54/6

Apply the fraction rule: -a/b = -a/b

= -54/6

Divide the numbers: 54/6 = 9

= -9

x = -9

Verify solutions

Find underfined (singularity) point: x = 0

Take the denominator (s) of - 54/x and compare to zero

x = 0

Combine undefined points with solutions:

x = -9

Substitute x = -9

[ o(-9) = 9]

Simplify

0(-9) = 9

Simplify

0(-9): -90

Remove parentheses: (-a) = -a

= -0 . 9

-90 = 9

[-90 = 9]

Isolate o for -90 = 9 : o = -1

-90 = 9

Divide both sides by -9

-90/-9 = 9/-9

Simplify

0 = -1

The solutions to the system of equations are:

x = -9, 0 = -1, x \ne 0

d.) circle motion requires a force to give it a centripetal acceleration.