Problem 115 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

The simplified expression is 14.

Step 1: 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].

Step 2: 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].

Step 3: 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).

Step 4: 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.