A few questions.

S

stef

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Nov 9, 2005
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I am preparing for a math 101 final at my college and need some help with a few problems.

1. x + 2 = 4(3x - 2)

I got the answer as a fraction: 10/11 = x

I arrived at that by combining like terms ..

x + 2 = 12x - 8
2 = 11x - 8
10 = 11x
10/11 = x

Is this correct?

2. 10 + 3x / (2 + 2x) when x = 5

I got:

10 + 15 / 2 + 2x
25 / 2 + 2x
12.5 + 2x

Is that right?

Thanks in advance!!
 
To check the solution to any "solving" exercise, plug the solution back into the original problem, and see if it works.

. . . . ."x + 2 = 4(3x - 2)", with x = 10/11:

. . . . .[10/11] + 2 = 4(3[10/11] - 2)
. . . . .10/11 + 22/11 ?=? 4(30/11 - 2)
. . . . .32/11 ?=? 120/11 - 8
. . . . .32/11 ?=? 120/11 - 88/11
. . . . .32/11 ?=? (120 - 88)/11
. . . . .32/11 ?=? 32/11

The solution checks.

I'm not sure what's going on with the other exercise...? I'd thought you were supposed to evaluate "when x = 5", but then you wouldn't have ended up with an "x" in the final answer, since all the x's would have been replaced with 5's. Sorry.

Eliz.

P.S. Thank you for formatting your work so nicely, and for showing your work! :mrgreen:
 
eek, I'm so sorry on that 2nd one! I don't know what I was thinking.

What I *meant* to say was:

10 + 3x / (2 + 2x) when x = 5

I got:

10 + 3(5) / (12)

10 + 15 / 12

25 / 12

X = 2.08333 ...

thanks again!
 
You posted:

. . . . .\(\displaystyle \large{10\mbox{ } +\mbox{ } \frac{3x}{2\mbox{ } +\mbox{ } 2x}}\)

...but you appear to have evaluated:

. . . . .\(\displaystyle \large{\frac{10\mbox{ } +\mbox{ } 3x}{2\mbox{ } +\mbox{ } 2x}}\)

FYI: Whichever form is correct, the answer should probably be given in "exact" (fractional) form, rather than approximate (decimal) form.

Eliz.
 
Ok, that makes sense.

My tutor and I came up with different answers, that's why I'm not getting it I think.

He came up with 5/4.

I came up with the decimal, but if I can't use that .. I come up with 25/12.
 
stef said:
Ok, that makes sense.
My tutor and I came up with different answers, that's why I'm not getting it I think.
He came up with 5/4.
I came up with the decimal, but if I can't use that .. I come up with 25/12.
Click to expand...

10 + 3x / (2 + 2x) when x = 5

Ok, you get 25/12, BUT that's the solution to (10 + 3x) / (2 + 2x) when x = 5 ;
(notice the extra brackets)
the solution for 10 + 3x / (2 + 2x) when x = 5 is 45/4 : tutor is wrong!

The brackets make a big difference: do you see that?

Take a simple example:
6+4/2 = 6 + 1/2 = 13/2
(6+4)/2 = 10 / 2 = 5 : clear nuff?
 
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