enter U if the equation has a unique solution, N if it has no solution, and I if it has infinitely many?

Question

1. 8x+3=9
2. 9x+8=9x+3
3. 1/8x+3=1/3x+9
4. 1/8x+3=2/8x+3
5. (x+8)(x+3)=x squared+11x+24
6. 2(8x+3)= 16x+6

no actually theyre not test answers...
how would i have the quiestions to the test....
duh

Answer 1

I

Answer 2

First, a little lesson in doing this.
When you use algebra to solve an equation, and you end up with x equaling one number (such as 0, 4, 3/2, 3.1415. . . . ), then the equation has a unique solution.

If you end up with a tautology such as 3 =3, or x = x, or x + 2 = x + 2, then there are infinitely many solutions, i.e. the equation will work with any real number.

If you end up with a false statement, such as 3 = 4, then the equation has no solution, meaning that no number will work.

That said,

1. 8x + 3 = 9 given
8x = 6 subtract 3 from both sides
x = 6/8 divide both sides by 8
x = 3/4 simplify
one unique solution

2. 9x + 8 = 9x =3 given
8 = 3 subtract 9x from both sides
this is a false statement, so this equation has no solution

3. 1/8x + 3 = 1/3x + 9 given
3x + 72 = 8x + 216
72 = 5x + 216
-144 = 5x
x = 144/5
U

4. 1/8x + 3 = 2/8x + 3
1/8x = 2/8x
0 = 1/8x
x = 0
U

5. (x + 8) (x + 3) = x^2 + 11 x + 24
x^2 + 11x + 24 = x^2 + 11 x + 24
both sides of the equation are identical, therefore it is a tautology, therefore the equation has infinitely many solutions

6. 2(8x + 3) = 16x + 6
16x + 6 = 16x + 6
infinitely many solutions

Answer 3

[EDITED]

You could have the test questions if you were taking the test on a computer and not properly supervised. Unfortunately, I see that happen at our school all the time. But I'll give you the benefit of the doubt. ;-)

I'm also going to assume that, in questions 3 & 4, the fractional coefficients such as 1/8 and 1/3 are supposed to be in parentheses, like this: (1/8)x. (Otherwise it looks like the x is in the denominator. Not your fault, just a side effect of the way Yahoo Answers doesn't allow proper math notation. ;-) )

If the two sides of an equation are identical, of course, the equation will have infinitely many solutions (I). Equations 5 & 6 fall under this category; in each case, if you expand the left side, you get the same expression that's on the right side.

Equation 2 has no solution (N), because there's no way that you can multiply some number by 9, and then get the same result whether you add 8 or 3 to it. As confirmation, when we subtract 9x from both sides, we get the equation 8=3, which is nonsense, so the answer to #2 is N.

The other three -- 1, 3, and 4 -- all have a Unique solution.

Hope that helps. :)

Answer 4

1) U
2) N
3) N
4) U
5) U
6) U

Answer 5

1.U
2.N
3.U
4.N
5.I
6.I