Formula Question

**Uriah5356** · March 11th 2009, 07:58 PM

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.

**sinewave85** · March 11th 2009, 08:18 PM

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:

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

**sinewave85** · March 11th 2009, 08:20 PM

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?

**Uriah5356** · March 11th 2009, 08:23 PM

Originally Posted by sinewave85

Where did you get a variable named x from?

For which question, those are two individual questions.

**sinewave85** · March 11th 2009, 08:24 PM

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.

**sinewave85** · March 11th 2009, 08:28 PM

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?

**e^(i*pi)** · March 11th 2009, 08:32 PM

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

**Uriah5356** · March 11th 2009, 08:47 PM

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!

**sinewave85** · March 11th 2009, 08:51 PM

Originally Posted by Uriah5356

Right!

Ok, now we are talking! First lets tackle the simplifications. Did you understand my first post?

**sinewave85** · March 11th 2009, 08:57 PM

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.

**sinewave85** · March 11th 2009, 09:13 PM

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.

**Uriah5356** · March 11th 2009, 09:13 PM

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

**Uriah5356** · March 11th 2009, 09:48 PM

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 ?

**sinewave85** · March 12th 2009, 08:05 AM

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.

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