Thread: Help: solving for x, writing interval notation and Absolute value inequities

Need Help with:

a)solving for x:

a-2[b-3(c-x)]=6

b)how do I write

0 ≥ x ≤ -2

in the <------------------------->

and in interval notation

c)How do I find the two answers to:

3-|2x+4| ≤ 1

I have read and tried following what my book said and I can't get the answers that appear in the book.

d)Is this correct:

solving for m:

$\displaystyle

F= G \frac {mM} {r^2}

$

$\displaystyle

m = \frac {Fr^2} {GM}

$

Originally Posted by Lonn

Need Help with:

a)solving for x:

a-2[b-3(c-x)]=6

Expand the brackets:

$\displaystyle a-2(b-3(c-x))=6 ~\implies~a-2(b-3c+3x))=6~\implies~a-2b+6c-6x=6$

Collect all terms containing x on the LHS and all other terms on the RHS of the equation. Divide by the leading factor of x.

b)how do I write

0 ≥ x ≤ -2

in the <------------------------->

and in interval notation

The wording of the problem must be wrong because you state there that $\displaystyle 0 \leq -2$

c)How do I find the two answers to:

3-|2x+4| ≤ 1

I have read and tried following what my book said and I can't get the answers that appear in the book.

$\displaystyle 3-|2x+4| \leq 1$
$\displaystyle 2 \leq |2x+4|$ Use the definition of the absolute value:
$\displaystyle |2x+4|=\left\{\begin{array}{lcr}2x+4&\implies & x\geq -2 \\ -(2x+4) &\implies & x < -2 \end{array}\right.$

Now solve for x:

$\displaystyle \left|\begin{array}{lcr}2 \leq 2x+4 &\wedge & x \geq -2 \\ 2 \leq -(2x+4) & \wedge & x <-2 \end{array}\right.$

d)Is this correct:

solving for m:

$\displaystyle

F= G \frac {mM} {r^2}

$

$\displaystyle

m = \frac {Fr^2} {GM}

$ <<<<<<< Yes

thanks I finally understand how absolute values work it was so simple and as you said my b) was wrong

I don't understand why the mathbooks used in school don't explain things in an easier way, the explanation on how to do things are all writen in mumbo jumbo lang you can't read anything just look at the numbers or you'll get confused. The Chemistry, Physics and Biology books I've used have all been very user friendly why can't they do that in math.

"Make everything as simple as possible, but not simpler." Albert Einstein

Originally Posted by Lonn

thanks I finally understand how absolute values work it was so simple and as you said my b) was wrong
I don't understand why the mathbooks used in school don't explain things in an easier way, the explanation on how to do things are all writen in mumbo jumbo lang you can't read anything just look at the numbers or you'll get confused. The Chemistry, Physics and Biology books I've used have all been very user friendly why can't they do that in math.

To be just brutally honest: Mathematicians cannot agree among ourselves on notation and definitions.
A simple example. You can get a real argument going over some simple questions.
“Is zero a natural number”?
“Is zero a counting number”?
“What is the difference among the sets: whole numbers, counting numbers, and/or natural numbers”?

Here is one from my own training: “Can there be an empty point-set?” One of the most important topologists of the last century said ‘absolutely not’. Professor Moore( any many of his students, my teachers) would not allow it used. (Keith Devlin has call R. L. Moore the greatest mathematics teacher.)

That was very interesting this "Moore method"

All of high school I only looked at an exercise and the answer on the back of the book and figured how to do it by myself

like in trigonometry all I used was the pitagoras theorem a2 + b2 = c2 for everything
I remember getting an exam in precalculus and not knowing anything and during the exam learning how to solve the exercises.

I only studied and used the text in the math book in my final exam.

But I have always had trouble whenever they ask for the procedure because mine is different from the teacher and everyone else and now in University they are asking for the procedure or the whole exercise is wrong and Im sure they wont accept mine specially in word problems.

Also in the precalculus exam I did the whole exam where they gave you the answers right just using what I knew of logic I dont know for sure because I didn't get what I got in each part but I believe I did get 80+% right.

But in the end they give you 3 exercises and tell you to solve them with procedures and I didn't know what to do because I didn't know the terms and what they where asking for. I would have really liked a teacher with that method.