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Chapter 0: Problem 115

Use the order of operations to simplify each expression. $$8-3[-2(2-5)-4(8-6)]$$

Short Answer

Expert verified
The simplified expression is 14.

Step by step solution

01

Simplify Inside Parentheses

First, simplify the expressions inside parentheses. In this case, we have two: (2 - 5) and (8 - 6). This gives us -3 and 2 respectively. The expression now becomes: 8 - 3[-2*(-3) -4*2].
02

Perform Multiplication

Next, perform multiplication. Inside the big brackets, you have -2 multiplied by -3, which gives 6. Also, -4 multiplied by 2 gives -8. Substituting these back into the expression, it becomes: 8 - 3[6 - 8].
03

Simplify Inside Brackets

Perform the operation inside the brackets, which is a subtraction. 6 - 8 gives -2. So, the expression now becomes: 8 - 3*(-2).
04

Perform Final Multiplication and Subtraction

Finally, perform the multiplication, 3 times -2 gives -6. Subtracting -6 from 8 gives you 14. So, the result of simplifying the expression is 14.

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