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Answer 1

a) 1 solution

b) infinite solutions

c) 1 solution

Explanation:

If you were to solve each of the problems:

1. "x = 10" would mean that there is only one solution: 10
2. "2 = 3" would mean that there are no solutions. These are not equal so the equation cannot be true regardless of the value of x.
3. "5 = 5" would mean that there are infinite solutions. The equation is true no matter what the value of x is.

a)

`2x+6=7x+5\\2x-7x=5-6\\-5x=-1\\5x=1\\x=(1)/(5)`

This equation only has one solution: 1/5.

b)

`6v+8=8+6v\\6v-6v=8-8\\0=0`

This equation has infinite solutions.

c)

`10-e=e-10\\10+10=e+e\\20=2e\\e=10`

This equation also only has 1 solution: 10.