Answer:
n = 2
Explanation:
Hi there!
We are given -(8-2n)=8-2(12-3n), which is an equation containing variables, and we want to solve the equation for the variable, which is n.
To do that, we want to isolate n on one side
This equation needs to be solved by the order of operations (PEMDAS, or parentheses, exponents, multiplication, division, addition, subtraction).
First, working from left to right, open up the parentheses on the left side by multiplying both 8 and -2n by -1 (the negative sign in front of the parentheses indicates -1(8-2n), or (8)(-1) + (-1)(-2n))
-1*8=-8
-1*-2n=2n
-8+2n = 8-2(12-3n)
Now on the right, it seems like we should subtract 2 from 8, then multiply the result by (12-3n), but remember we still have parentheses to deal with.
So multiply both 12 and -3n by -2, then add the numbers together
12*-2=-24
-3n*-2=6n
-24+6n
Remember that we didn't do anything to 8, so the equation so far is:
-8+2n=8-24+6n
Now we can start to isolate n on one side (leave n by itself on one side)
Remember we're still working from left-right
So remove -8 from the left by adding it to both sides (-8+8=0)
-8+2n=8-24+6n
+8 +8
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0 + 2n=16-24+6n
Now we can subtract 24 from 16
0 + 2n = -8 + 6n
Now, we still have 6n on the right, and remember; we want to isolate n on one side.
So let's remove it from the right by subtracting 6n from both sides
0 + 2n = -8+6n
-6n -6n
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-4n = -8
Now we have the expressions containing variables on the left and the numbers on the right. However, remember we just want a singular n by itself, not -4n.
A singular n is also 1n, since 1 * any number = that number
So divide both sides by -4 to find what the value of 1n is
n = 2
Hope this helps!