I need help on my geometry homework..?

Question

i don't really understand these problems i finished all of it, but i just need these..

It says:

Draw a sketch to illustrate each postulate.

16. If two planes intersect, then their intersection is a line.

Decide whether the statement is true or false. If false, provide a counterexample.

6) The equation 4x - 3 = 12 + 2x has exactly one solution.

11) The equation 2x - 7 = 5 + x has exactly one solution.

I would love it if you show some work so it would help me understand it.

Thanks!!! <333333333

Answer 1

6) The equation 4x - 3 = 12 + 2x has exactly one solution.

2x = 15

x = 15/2

True

11) The equation 2x - 7 = 5 + x has exactly one solution.

x - 7 = 5

x = 12

True

If the answer had been, say, 8 = 3 (which is never true), it would have no solution.

If the answer had been, say, 8 = 8 (which is always true), it would have infinitely many solutions...which is more than exactly one solution. You could plug in any number for x and it would be true, then pick any different number for x and it would also be true...and that would be a counterexample.

Hope that helps!