# Some complex review questions

• Nov 13th 2007, 02:56 PM
Nightfire
Some complex review questions
Ok, we had a sub today so i couldnt ask then, and almost all of the class was stumped by these questions, so i thought i'd post them here... literally everyone was complaining about them at some point. (note: things such as 1/2 and 3/4 are fractions.)
-5= 3/8(x-1)

8x+6=3(4-x)

these next few were just unexplained to us...they may be easy, who knows

4(1/2x + 1/2) = 2x+2

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

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

-4(x-3) = 6(x+5)
• Nov 13th 2007, 03:13 PM
Jonboy
to solve the unexplained problems you need to use the distributive property.

Basically what it is, if you have a(b + c) it is equal to multiplying the a by the two terms in the parenthesis, b and c.

In other words, a(b + c) = ab + ac

When you multiply fraction, you multiply both the tops and both the bottoms of the fraction.

So like if you had: $\frac{1}{2}\cdot\frac{1}{8}$ the answer would be $\frac{1 * 1}{2 * 8}\,=\,\frac{1}{16}$

Use this to attempt these problems, and we'll tell you if they are correct.
• Nov 13th 2007, 04:13 PM
Nightfire
ok, lets see..

8x+6=3(4-x)
8x+6=12-3x
11x+6=12
11x=6
x=.54(repeating)

4(1/2x + 1/2) = 2x+2
4/1x + 4/1=2x+2
4x+4=2x+2
2x+4=2
2x=-2
x=1

-3(-x-4)=2x+1
3x+12=2x+1
x+12=1
x=-11

4x=-2(-2x+3)
4x=4x-6
4x-4x=0x?
0x=-6

-4(x-3)=6(x+5)
-4x+12=6x+30
12=10x+30
-18=10x
-1.8=x

-5=3/8(x-1)
-5=3/8x-.375
-5.375=3/8x
-14.3(repeating)=x

i dont think i got some of them..we've never gotten decimal answers before
• Nov 13th 2007, 06:39 PM
topsquark
8x+6=3(4-x)
8x+6=12-3x
11x+6=12
11x=6
x=.54(repeating)
Good!

4(1/2x + 1/2) = 2x+2
4/1x + 4/1=2x+2
$4 \left ( \frac{1}{2}x + \frac{1}{2} \right )$

$= 4 \cdot \frac{1}{2}x + 4 \cdot \frac{1}{2}$

$= 2x + 2$

So 2x + 2 = 2x + 2. What does this tell you about the possible values for x?

-3(-x-4)=2x+1
3x+12=2x+1
x+12=1
x=-11
Good!

4x=-2(-2x+3)
4x=4x-6
4x-4x=0x?
0x=-6
Good so far.

What does 0 = -6 tell you about possible values of x and whether this "equation" can possibly be true?

-4(x-3)=6(x+5)
-4x+12=6x+30
12=10x+30
-18=10x
-1.8=x
Good!

-5=3/8(x-1)
-5=3/8x-.375
-5.375=3/8x
$-5 = \frac{3}{8}x - .375$

$-5 + .375 = \frac{3}{8}x - .375 + .375$

$-4.625 = \frac{3}{8}x$

Quote:

Originally Posted by Nightfire
i dont think i got some of them..we've never gotten decimal answers before

I am surprised that your instructor is even allowing decimal answers. Fractions are not nearly as frightening if you work with them for a while. In addition, decimal answers are commonly left as an approximation to the answer, which can typically be written as a fraction.

Use fractions.

-Dan
• Nov 13th 2007, 07:17 PM
Nightfire
Quote:

4(1/2x + 1/2) = 2x+2
4/1x + 4/1=2x+2
$4 \left ( \frac{1}{2}x + \frac{1}{2} \right )$

$= 4 \cdot \frac{1}{2}x + 4 \cdot \frac{1}{2}$

$= 2x + 2$

So 2x + 2 = 2x + 2. What does this tell you about the possible values for x?

I'm gonna go with All Real Numbers.

Quote:

4x=-2(-2x+3)
4x=4x-6
4x-4x=0x?
0x=-6
Good so far.

What does 0 = -6 tell you about possible values of x and whether this "equation" can possibly be true?
I'm gonna go with the opposite of All Real Numbers. No Solution or something, lol

Quote:

-5=3/8(x-1)
-5=3/8x-.375
-5.375=3/8x
$-5 = \frac{3}{8}x - .375$

$-5 + .375 = \frac{3}{8}x - .375 + .375$

$-4.625 = \frac{3}{8}x$
We never even touched this...why is it on a 'review' sheet?

I can usually get the No Solutions/All Real Numbers questions, i just get confused because they seem to be thrown in randomly..theres an entire page of answered questions with 'x=#' as the answer, and then out of nowhere one that just doesnt seem to work...it seems like they should warn you its going to be a NS/ARN problem, but that'd be too simple.
why isn't math as easy as language? if that were the case i wouldnt even need these forums, i'm making 10% higher than the class average in language, and the class average is 87.5% :p
• Nov 14th 2007, 05:15 AM
topsquark
Quote:

Originally Posted by Nightfire
I'm gonna go with All Real Numbers.

I'm gonna go with the opposite of All Real Numbers. No Solution or something, lol

Yup to both.

Quote:

Originally Posted by Nightfire
We never even touched this...why is it on a 'review' sheet?

Never touched this? This is simply a linear equation in one variable. The only complication is the one you introduced: mixing the decimals and the fractions. Here's how I would have handled this:
$-5 = \frac{3}{8}(x - 1)$

First, get rid of that pesky fraction by multiplying both sides by 8:
$8 \cdot -5 = 8 \cdot \frac{3}{8}(x - 1)$

$-40 = 3(x - 1)$

Does this look more familiar?

Quote:

Originally Posted by Nightfire
I can usually get the No Solutions/All Real Numbers questions, i just get confused because they seem to be thrown in randomly..theres an entire page of answered questions with 'x=#' as the answer, and then out of nowhere one that just doesnt seem to work...it seems like they should warn you its going to be a NS/ARN problem, but that'd be too simple.
why isn't math as easy as language? if that were the case i wouldnt even need these forums, i'm making 10% higher than the class average in language, and the class average is 87.5% :p

Math is a language, it's just that many High School level students (especially in the US) haven't been taught how to think in terms of Mathematical logic. A good strategy for this case is to remember how to solve the equations. If you get 0 = 0 at the end, then the solution is all real numbers. (Actually all numbers, no matter what system you are using.) If you get x = #, then you have only one solution (this is called a "conditional" equation.) If you get something like 0 = -6, then you have a contradiction and no value of x will solve the equation.

Just remember those and you will do fine for now.

-Dan