Question

Evaluate each expression. $$ 2 \cdot[8-3(4+2)]-3 $$

Short answer

-23

Step-by-step solution

- Simplify Inside Parentheses

First, solve the expression inside the innermost parentheses: \(4 + 2\) gives 6.

- Multiply Inside Brackets

Next, multiply the result by 3: \(3 \times 6 = 18\). Substitute back into the bracketed expression: \(8 - 18\).

- Simplify Bracket

Now simplify the expression inside the brackets:\(8 - 18 = -10\).

- Multiply Outside Brackets

Multiply the resulting value by 2: \(2 \times -10 = -20\).

- Subtract the Final Value

Finally, subtract 3 from the result: \(-20 - 3 = -23\).

Key concepts

parentheses

Parentheses are the first part of the order of operations we need to tackle. They are used to group parts of an expression that should be solved before anything else.
In the expression given, we see parentheses in the term \(4 + 2\).
This tells us to solve \(4 + 2\) first. Once simplified, \(4 + 2\) becomes 6.

By simplifying the innermost parentheses first, we make the overall expression simpler and easier to manage.
Always remember, any operation inside parentheses should be performed before moving on to other parts of the equation.

multiplication

After handling parentheses, the next step is multiplication. Multiplication usually comes before addition and subtraction, based on the rules of the order of operations.
In the expression, after simplifying inside the parentheses, we had the term \(3 \times 6\). This is the multiplication we need to solve next.

Multiplying the numbers inside gives us \(3 \times 6 = 18\). This result is then substituted back into the remaining expression inside the brackets to simplify further.
Remember: When you have multiple operations, always handle multiplication before moving on to addition or subtraction.

addition and subtraction

Finally, let's discuss addition and subtraction. These are often the last operations performed in an expression based on the order of operations.
In our example, after simplifying the parentheses and performing multiplication, we dealt with the bracketed expression \(8 - 18\), simplifying it to \(-10\).
After that, we managed the subtraction outside the brackets—first multiplying \(-10\) by 2 to get \(-20\), and then doing the subtraction \(-20 - 3 = -23\).

This step-by-step approach ensures clarity and accuracy in solving expressions. It's key to remember to perform addition and subtraction after handling parentheses and multiplication.