How many solutions does -2z+2+4z=16/5+2z-6/5

Infinite. Please Mark Brainliest, this took a lot of effort.

Step-by-step explanation:

After going through the process of solving, you get 0=0, meaning true for all z

-2z+2+4z=16/5+2z-6/5

Group Like Terms

-2z+4z+2=16/5+2z-6/5

Add similar terms

2z+2=16/5+2z-6/5

Group Like Terms

2z+2=2z-6/5+16/5

Combine the Fractions

Apply the rule a/c plus or minus b over c equals a plus or minus b over c

=(-6+16)/5

Add/Subtract the numbers

=10/5

Divide the numbers

=2

2z+2=2z+2

Subtract 2 from each side

2z+2-2=2z+2-2

Simplify

2z=2z

Subtract 2z from each side

2z-2z=2z-2z

Simplify

0=0

Both sides are equal, true for all z

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

  the correct choice is marked

step-by-step explanation:

the first two graphs show multiple turning points. the last graphs matches the description in every detail.