SOLUTION: Simplify: 14 - (10 - (3x - 7) - 8x). Please include clear working out. Thanks!

Question 1005266: Simplify: 14 - (10 - (3x - 7) - 8x).
Please include clear working out. Thanks!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
removing parentheses can be tricky.

start with:

14 - (10 - (3x - 7) - 8x)

you want to process the innermost parentheses first, then the next most innermost, then the next most innermost, until you have no nested parentheses left to operate on.

so we work on the most nested parentheses first, which is (3x - 7)

processing the parentheses means performing the intended operation on the expression within the parentheses.

in this case the operation is - (3x - 7)

that's the same as -1 * (3x - 7)

perform that operation and you get -3x + 7

your expression becomes:

14 - (10 - 3x + 7 - 8x)

you now operate on your next most inner parentheses.

that expression is (10 - 3x + 7 - 8x).

once again, the operation to be performed is - (10 - 3x + 7 - 8x).

this is the same as -1 * (10 - 3x + 7 - 8x).

perform the operation and you get -10 + 3x - 7 + 8x.

your expression becomes:

14 - 10 + 3x - 7 + 8x.

regroup the terms to get:

(14 - 10 - 7) + (3x + 8x)

combine the like terms within each set of parentheses and remove the parentheses to get:

-3 + 11x

that should be your solution.

a way to check is to use your scientific calculator that has the capability to solve expressions within parentheses.

let x = any arbitrary value and then solve the final expression and then solve the original expression.

you should get the same answer.

for example:

we'll let x = 20

final expression is -3 + 11x which is equal to -3 + 11*20 which is equal to -3 + 220 which is equal to 217.

original expression is 14 - (10 - (3x - 7) - 8x) which becomes equal to:

14 - (10 - (3*20 - 7) - 8*20) which becomes equal to:

14 - (10 - (60 - 7) - 160).

stick that in your calculator as is and the answer will be:

217.

same answer either way means you did good.

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