# Math Help - Formula Question

1. ## Formula Question

Alright so I have two equations that the paper is giving me to simplify, only problem is I don't know where to start.. and my text book isn't being helpful, so I was wondering if anyone could point me in the right direction? x.x

2/3 (12t - 18) + 2t - 30

40 ( 3/8 * Y - 1/4) + 40 (4/5)

It is also asking me to solve for questions.

2 - (4x + 7) = 3 + 2 (x + 2) ------ I started solving this one by using distributive property after adding 3+2=5 on the right side, making (x + 2) into 5x + 10..?

x/3 + x/4 = -2 ------ This one I started by getting the least common denominator of 3 and 4, which made the equation 4x/12 + 3x/12 = 7x/12 ------ From there it left me with 7x/12 = -2 and from there I am stuck.

2. Originally Posted by Uriah5356
Alright so I have two equations that the paper is giving me to simplify, only problem is I don't know where to start.. and my text book isn't being helpful, so I was wondering if anyone could point me in the right direction? x.x

2/3 (12t - 18) + 2t - 30

40 ( 3/8 * Y - 1/4) + 40 (4/5)
First you need to multiply throught the parentheses:

$\frac{2}{3}(12t - 18) +2t -30 = \left(\frac{2}{3}\right)(12t) - \left(\frac{2}{3}\right)(18) + 2t - 30 = 8t -12 +2t - 30$

Then you can just add like terms:

$8t -12 +2t - 30 = 10t -42$

3. Originally Posted by Uriah5356
Alright so I have two equations that the paper is giving me to simplify, only problem is I don't know where to start.. and my text book isn't being helpful, so I was wondering if anyone could point me in the right direction? x.x

2/3 (12t - 18) + 2t - 30

40 ( 3/8 * Y - 1/4) + 40 (4/5)

It is also asking me to solve for questions.

2 - (4x + 7) = 3 + 2 (x + 2) ------ I started solving this one by using distributive property after adding 3+2=5 on the right side, making (x + 2) into 5x + 10..?

x/3 + x/4 = -2 ------ This one I started by getting the least common denominator of 3 and 4, which made the equation 4x/12 + 3x/12 = 7x/12 ------ From there it left me with 7x/12 = -2 and from there I am stuck.

Where did you get a variable named x from?

4. Originally Posted by sinewave85
Where did you get a variable named x from?
For which question, those are two individual questions.

5. Originally Posted by sinewave85
First you need to multiply throught the parentheses:

$\frac{2}{3}(12t - 18) +2t -30 = \left(\frac{2}{3}\right)(12t) - \left(\frac{2}{3}\right)(18) + 2t - 30 = 8t -12 +2t - 30$

Then you can just add like terms:

$8t -12 +2t - 30 = 10t -42$
Continuing from here, asuming you want to find the zeros of the function $f(t) = \frac{2}{3}(12t - 18) +2t -30$

$f(t) = 10t - 42$

$0 = 10t - 42$

$42 = 10t$

$t = \frac{42}{10} = \frac{21}{5} = 4.2$

Edit: Ignore all of this. I was confused by the OP's edit and thought that he or she wanted to solve the original expressions posted.

6. Originally Posted by Uriah5356
For which question, those are two individual questions.
Ok, after rereading: The first two expressions you only need to simplify, the second set you need to solve, right?

7. Originally Posted by Uriah5356

2 - (4x + 7) = 3 + 2 (x + 2) ------ I started solving this one by using distributive property after adding 3+2=5 on the right side, making (x + 2) into 5x + 10..?

x/3 + x/4 = -2 ------ This one I started by getting the least common denominator of 3 and 4, which made the equation 4x/12 + 3x/12 = 7x/12 ------ From there it left me with 7x/12 = -2 and from there I am stuck.
2 - 4x - 7 = 3+2x+4 (multiplying comes before addition)

6x = -12
x = -12/6 = -2

----

From 7x/12 = -2 all you need to do it multiply -2 by 12/7

8. Originally Posted by sinewave85
Ok, after rereading: The first two expressions you only need to simplify, the second set you need to solve, right?
Right!

9. Originally Posted by Uriah5356
Right!
Ok, now we are talking! First lets tackle the simplifications. Did you understand my first post?

10. Originally Posted by sinewave85
First you need to multiply throught the parentheses:

$\frac{2}{3}(12t - 18) +2t -30 = \left(\frac{2}{3}\right)(12t) - \left(\frac{2}{3}\right)(18) + 2t - 30 = 8t -12 +2t - 30$

Then you can just add like terms:

$8t -12 +2t - 30 = 10t -42$
Lets pick up again from here. Sorry about the confusion. The key to simplifying the first two expressions is the distributive property, which is very nicely explained here: Distributive Property - Free Math Help. After that, it is just a matter of adding like terms.

11. Here is the second expression simplified:

$40\left(\frac{3}{8}Y - \frac{1}{4}\right) + 40\left(\frac{4}{5}\right) = 40\left(\frac{3}{8}Y\right) - 40\left(\frac{1}{4}\right) + 40\left(\frac{4}{5}\right) = 15Y - 10 + 32 = 15Y +22$

Unfortunately, I don't have time to completely go through the third and fourth problems, but e^(i*pi) did a nice job of typing them out. You need to review how the distributive property relates to the order of opperations --why you can't add the 3 and the 2 outside the parentheses first here: $3 + 2(x + 2)\not= 5(x +2)$. I think that website I put up the link to will help. If this can wait untill tomorrow, I can work with you more then. Just reply and let me know where you are at.

12. Thanks for the help on these problems. :< I will be up for awhile so I might have more.

13. Originally Posted by e^(i*pi)
2 - 4x - 7 = 3+2x+4 (multiplying comes before addition)

6x = -12
x = -12/6 = -2

----

From 7x/12 = -2 all you need to do it multiply -2 by 12/7

Why reverse 7/12 to 12/7 to multiply? o.o
Am I correct in getting -24/7 ?

14. Originally Posted by Uriah5356
Why reverse 7/12 to 12/7 to multiply? o.o
Am I correct in getting -24/7 ?
Because you are really not multiplying, you are dividing both sides of the equation by 7/12 (because division undoes the multiplication by 7/12 on the left side of the equation). But to divide by a fraction, you invert the fraction (swap the numerator and the divisor) and rewrite the division as a multiplication like this:

$\frac{7x}{12} = -2$

$\frac{\frac{7x}{12}}{\frac{7}{12}} = \frac{-2}{\frac{7}{12}}$

$\left(\frac{7x}{12}\right)\left(\frac{12}{7}\right ) = \left(-2\right)\left(\frac{12}{7}\right)$

$\mbox{note}\uparrow\mbox{how dividing 7/12 by itself cancels it out and leaves x by itself}$

$x = \frac{-24}{7}$

Yes, you are correct in getting -27/7 .

P.S. Don't forget to hit the Thanks button at the bottom of useful posts.