Problem 4 - Elementary Algebra

Question

Use the grouping symbols to help perform the following operations. $$6\\{2[2(10-9)]\\}$$

Step-by-Step Solution

Answer

Answer: The simplified form of the expression is 24.

Step 1: Identify the innermost grouping symbols

First, we'll look for the innermost grouping symbols, which in this case are the parentheses. We'll start by simplifying the expression inside the parentheses.

Step 2: Simplify the expression inside the parentheses

We see \((10-9)\) inside the parentheses. Subtracting 9 from 10, we get: $$2[2(1)]$$

Step 3: Identify the next set of grouping symbols

Now that the expression inside the parentheses has been simplified, we'll move on to the next set of grouping symbols - the square brackets.

Step 4: Simplify the expression inside the square brackets

We now have \(2[2(1)]\). Multiplying 2 times 1, we get: $$2[2]$$

Step 5: Simplify the expression inside the curly braces

Finally, we can simplify the expression inside the curly braces, which is now \(6\{2[2]\}\). We see that we can further multiply 2 times 2 which results in: $$6\{4\}$$

Step 6: Simplify the entire expression

Now we just need to multiply 6 times the number inside the curly braces (4): $$6\cdot 4 = 24$$ So the simplified expression is: $$24$$