# Math Help - Some complex review questions

1. ## 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)

2. 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.

3. 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

4. 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
$-5 = \frac{3}{8}x - .375$

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

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

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

5. 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.

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

-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%

6. 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.

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?

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%
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