Problem 7 - Elementary Algebra

Question

Use the order of operations to find each value. $$2+3(18-5 \cdot 2)$$

Step-by-Step Solution

Answer

Answer: The value of the expression is 26.

Step 1: Identify the operation inside the parentheses.

First of all, identify the operation that is inside the parentheses: $$2+3(18-5 \cdot 2)$$ In this case, it's \((18-5 \cdot 2)\). Now, perform the operations inside the parentheses following the order of operations.

Step 2: Perform multiplication inside the parentheses.

The expression inside the parentheses is \(18-5 \cdot 2\). According to the order of operations, perform multiplication first: $$18 - 5 \cdot 2 = 18 - 10$$ Now the expression inside the parentheses becomes \((18 - 10)\).

Step 3: Perform subtraction inside the parentheses.

Next, perform the subtraction inside the parentheses: $$18 - 10 = 8$$ Now the original expression becomes: $$2+3(8)$$

Step 4: Perform multiplication.

Now, perform the multiplication of \(3(8)\): $$3 \cdot 8 = 24$$ So the expression becomes: $$2+24$$

Step 5: Perform addition.

Finally, perform the addition: $$2 + 24 = 26$$ The value of the given expression, after applying the order of operations, is 26.