1. ## needing some understanding

.3x = -12
well somehow I dont understand the mathmatics about how this equation is translated. well in order to get rid of the x... we.3x/.3.dont understand.
then we, I think .3x/3 = -12/.3 the answer is -40. well first I dont understand why we divide .3x/3 and get .3 second, Idont uderstand how -12/.3 =-40. doesnt -12/.3 =-.4 if you can explain . this would help me understand the process . ps my book says the answer is -40

2. Originally Posted by Leona_Marie
.3x = -12
well somehow I dont understand the mathmatics about how this equation is translated. well in order to get rid of the x... we.3x/.3.dont understand.
then we, I think .3x/3 = -12/.3 the answer is -40. well first I dont understand why we divide .3x/3 and get .3 second, Idont uderstand how -12/.3 =-40. doesnt -12/.3 =-.4 if you can explain . this would help me understand the process . ps my book says the answer is -40
$\displaystyle 0.3x = -12$

Now, if you realise that $\displaystyle 0.3 = \frac{3}{10}$, then the equation can be written as:

$\displaystyle \frac{3}{10}x = -12$

We need to get rid of the 3 and the 10 on the left hand side. The 10 is on the denominator, so to get rid of it, we need to multiply the expression by 10. But if we do that, we must ALSO multiply the right hand side of the equation by 10:

$\displaystyle 10 \times \frac{3}{10}x = 10 \times (-12)$

Now on the LHS, the 10s on the top and bottom will cancel, leaving:

$\displaystyle 3x = -120$

Now we need to get rid of that 3. It's in the numerator, so to get rid of it, we must divide the LHS by 3, and we must also do that to the RHS.

$\displaystyle \frac{3x}{3} = \frac{-120}{3}$

The 3s on the LHS will cancel, and you should be able to calulate the RHS!

$\displaystyle x = -40$

3. Originally Posted by Leona_Marie
.3x = -12
well somehow I dont understand the mathmatics about how this equation is translated. well in order to get rid of the x... we.3x/.3.dont understand.
then we, I think .3x/3 = -12/.3 the answer is -40. well first I dont understand why we divide .3x/3 and get .3 second, Idont uderstand how -12/.3 =-40. doesnt -12/.3 =-.4 if you can explain . this would help me understand the process . ps my book says the answer is -40
To solve this equation it is necessary to get the factor 1 (one) in front of the x, because you want to know the value of one x.

If you divide a number by itself the result is 1 (one). (Don't try this with the number 0, because the division by zero is forbidden). Therefore divide the complete equation by the leading factor of x:

$\displaystyle \dfrac{0.3 \cdot x}{0.3} = \dfrac{-12}{0.3}$

At the LHS you can cancel rhe 0.3 and you'll get:

$\displaystyle 1 \cdot x = \dfrac{-12}{0.3}$

To get rid of the decimal number in the denominator multiply the RHS by $\displaystyle \frac{10}{10}$

$\displaystyle 1 \cdot x = \dfrac{-12}{0.3} \cdot \frac{10}{10}$

$\displaystyle x = \dfrac{-120}{3} = -40$

4. Originally Posted by earboth
To solve this equation it is necessary to get the factor 1 (one) in front of the x, because you want to know the value of one x.

If you divide a number by itself the result is 1 (one). (Don't try this with the number 0, because the division by zero is forbidden). Therefore divide the complete equation by the leading factor of x:

$\displaystyle \dfrac{0.3 \cdot x}{0.3} = \dfrac{-12}{0.3}$

At the LHS you can cancel rhe 0.3 and you'll get:

$\displaystyle 1 \cdot x = \dfrac{-12}{0.3}$

To get rid of the decimal number in the denominator multiply the RHS by $\displaystyle \frac{10}{10}$

$\displaystyle 1 \cdot x = \dfrac{-12}{0.3} \cdot \frac{10}{10}$

$\displaystyle x = \dfrac{-120}{3} = -40$
thank you for helping me understand that 0.3x/0.3... I dont mean to belabor, but how does.3 x x =-12 does -120 just reduce down. is -120 the same as -12. because .3 x -4 = -12. no

5. Originally Posted by Leona_Marie
thank you for helping me understand that 0.3x/0.3... I dont mean to belabor, but how does.3 x x =-12 does -120 just reduce down. is -120 the same as -12. because .3 x -4 = -12. no
x has the value -40. And $\displaystyle 0.3 \cdot (-40) = -12$ .