SOLUTION: Solve showing all work. 3n - 5= -8(6 + 5n)

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Question 822032: Solve showing all work.
3n - 5= -8(6 + 5n)



Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
Here are some steps you can use for equations like this:
  1. Simplify:
    • Go through the order of operations (aka PEMDAS) on each side.
    • (Optional) Eliminate fractions or decimals by multiplying each side by an appropriate expression.
  2. Make sure the variable is on only one side of the equation. This is done by adding or subtracting an appropriate expression to eliminate the variable term(s) on the "other" side. Hint: Keep the variable term with the larger coefficient.
  3. Isolate the variable:
    1. On the side of the equation where is variable is, eliminate any terms (by adding or subtracting) which do not have the variable in them.
    2. If there are multiple, unlike terms with the variable, factor the variable out from these terms.
    3. If the variable is multiplied by anything but a 1, divide both side by that expression (or multiply by its reciprocal).
Let's see this work on your equation:
3n - 5 = -8(6 + 5n)
1. Simplify.
On the left there is nothing which can be done since the terms are not like terms. On the right we can use the Distributive Property to multiply by -8:
3n - 5 = -48 + (-40n)
2. Ensure the variable is on just one side.
The variable, n, is on both sides. Since 3 is larger than -40 I will keep the 3n. Adding 40n (to make -40n disappear on the right side):
43n - 5 = -48
3. Isolate the variable.
3.1 Eliminate extra terms.
The -5 is on the same side of the equation as the variable. It needs to go. Adding 5 to each side:
43n = -43
3.2 Factor the variable (if it is in multiple, unlike terms.
The variable is in just one term.
3.3 Divide by what the variable is being multiplied by (or multiply by its reciprocal).
Dividing by 43 (or multiplying by 1/43) we get:
n = -1
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