# How to solve the equation $8(12x + 15) + 13(2x - 11) = 123$

I'm doing some revision again and I need a bit of help. I've doing some a bit of equations from a textbook and I'm not sure how to solve it.

You need to find the $x$ so how would you solve $8(12x + 15) + 13(2x - 11) = 123.$

I know you should expand the brackets but after that nothing's adding up.

$1.$ $8(12x + 15) + 13(2x - 11) = 123.$

$2.$ $96x + 120 + 26 x - 143$ Expand the brackets and then that's when I'm a bit stuck with the positive and negative...

$3.$ $122x + - 23$. I don't know what do after that, I'm not even sure if it's $-23$ (pretty positive it's wrong.) Would I do $123 - 23$??? Any help?

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You have $122x-23=123$, so $122x=146$ and... – Dennis Gulko Jun 1 '13 at 7:42
I just want to give you a huge thank you for showing your work, and explaining your thoughts about the problem! Far too few people do it, and it really makes people happy to help, and lets them write answers that will be more useful to you. Please keep it up! – Zev Chonoles Jun 1 '13 at 7:45
But I'm trying to find $x$... – user61406 Jun 2 '13 at 7:46

Everything you did was correct! You have applied the distributive law: $$a(b+c)=ab+ac,$$ and also used that $$a-b=a+(-b)$$ (subtracting a number is the same as adding its negative). Your steps are \begin{align*} 8(12x + 15) + 13(2x - 11) &= 123\\\\ 96x + 120 + 26 x - 143 &=123\\\\ 122x - 23&=123 \end{align*} Our goal is ultimately to get $x$ all by itself, so how can we remove the extra stuff on the left side? Remember, we can do anything we want as long as we do it to both sides of the equation, so the first thing to do would be to add $23$ to both sides, because this will cancel out the negative $23$ that's currently on the left side. Do you see how do deal with the $122$?

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$122x = 146$. I know that you devide but if I devide the two numbers together it doesn't make the right number. – user61406 Jun 1 '13 at 8:06
@HonkyHanka: What are you using to determine what the "right" number is? If there's a given answer, it could be wrong, or perhaps you've copied the question down incorrectly. – Zev Chonoles Jun 1 '13 at 8:11
Well i'm trying to find the $x$ so when I added into the equation I get the answer $123$. – user61406 Jun 1 '13 at 9:24
After dividing both sides of the equation $$122x=146$$ by $122$, we get $$x=\frac{146}{122}=\frac{73}{61}.$$ That is the right number. Perhaps your calculations when you plug this number into the original equation are incorrect. – Zev Chonoles Jun 1 '13 at 9:30

$$96x + 120 + 26 x - 143=123$$ from this step, our goal is to separate out different type of terms on each side of equal sign so I am moving the terms containing $x$ to Left and numbers to the right side.When we transfer any thing to from any side to other side it will changes its sign positive thing become negative and vice versa and multiplication become division and vice versa.so I'm trying to make you clear this thing. $$96x + 120 + 26 x - 143=123$$ All terms of x is already on same side so there isn't any need to touch it just settle the numbers. $$96x +26 x =123+ 143-120$$

Here is what happened $120$ is in addition and it have positive value so it will become $-120$ to the other side similarly $143$ has negative sign so it become positive on the other side.

Then if two number has same sign they will add and take their sign. $$122 x =266-120$$

Here $122$ and $143$ have same sign + so they add and have + sign (we don't right + sign it is understandable) $$122 x =146$$ Here $266$ and $120$ has different sign so smaller one substract from larger one and place larger values sign to answer.(if this will write as $-120+266\;$it is also $146$ ). $$x=\dfrac{146}{122}$$ Here we want to alone $x$ so try to $122$. This is in multiplication with $x$ so on the other side it will become in division.

We can divide the answer from $2$ so it will $$x=\dfrac{146}{122}\implies x=\dfrac{73}{61}$$

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