Problem 111 - Intermediate Algebra

Question

In the following exercises, simplify each expression. $$ 9-2[3-8(-2)] $$

Step-by-Step Solution

Answer

The simplified expression is $$ -29 $$

Step 1 - Simplify inside the parentheses

First, simplify the expression inside the parentheses. Within the brackets we have Simplify the multiplication inside: $$ -8(-2) = 16 $$ Now the expression is: $$ 9 - 2[3 + 16] $$

Step 2 - Perform the addition inside the brackets

Next, add the numbers inside the brackets: $$ 3 + 16 = 19 $$ Now the expression is: $$ 9 - 2[19] $$

Step 3 - Simplify the multiplication outside the brackets

Perform the multiplication outside the brackets: $$ 2 \times 19 = 38 $$ Now the expression is: $$ 9 - 38 $$

Step 4 - Subtract the result

Finally, subtract to get the answer: $$ 9 - 38 = -29 $$

Key Concepts

order of operations

To simplify any algebraic expression correctly, follow the order of operations. This rule is often remembered by the acronym PEMDAS:

• Parentheses
• Exponents
• Multiplication and Division
• Addition and Subtraction

This order ensures you perform arithmetic in the correct sequence.
In our example, we start with parentheses, then handle multiplication, addition, and lastly, subtraction.

parentheses

Parentheses are the first priority in the order of operations. They signal that everything inside should be simplified before moving on to other operations. In the problem $$9 - 2[3 - 8(-2)]$$, we begin by simplifying the expression within the brackets.
Start here: $$3 - 8(-2)$$. This step is essential for ensuring accuracy.

multiplication

Multiplication should be done before addition or subtraction, after taking care of any parentheses. In the expression inside the parentheses $$3 - 8(-2)$$, we first handle the multiplication:
$$-8(-2) = 16$$. Now the expression looks like this: $$3 + 16$$.
Trust this sequence; it saves you from mistakes.

addition

Once the multiplication is handled, move on to any addition within the parentheses. For our example, after multiplication we have:
$$3 + 16$$. Simplify this to get $$19$$.
This makes the expression $$9 - 2[19]$$. Don't rush; follow the order carefully.

subtraction

After dealing with parentheses, multiplication, and addition, finally handle subtraction. In our expression, we now have:
$$9 - 2(19)$$.
First, simplify the term involving multiplication:
$$2 \times 19 = 38$$.
This leaves us with:
$$9 - 38$$.
Finish by performing the subtraction:
$$9 - 38 = -29$$.
Applying these steps methodically ensures you arrive at the correct answer.