Problem 9 - Elementary Algebra

Question

Use the order of operations to find each value. $$\frac{19+2\\{5+2[18+6(4+1)]\\}}{5 \cdot 6-3(5)-2}$$

Step-by-Step Solution

Answer

Question: Evaluate the given expression: $$\frac{19+2\{5+2[18+6(4+1)]\}}{5 \cdot 6-3(5)-2}$$ Answer: $$\frac{221}{13}$$

Step 1: Solve the inner-most parentheses

We first solve the operations inside the inner-most parentheses \((4+1)\): $$\frac{19+2\\{5+2[18+6(5)]\\}}{5 \cdot 6-3(5)-2}$$

Step 2: Solve the brackets

Now, we will solve the operations inside the brackets \([18+6(5)]\): $$\frac{19+2\\{5+2[48]\\}}{5 \cdot 6-3(5)-2}$$

Step 3: Solve the braces

Next, we will solve the operations inside the braces \(\{5+2[48]\}\): $$\frac{19+2\\{101\\}}{5 \cdot 6-3(5)-2}$$

Step 4: Solve the remaining operations in the numerator

Now, we will solve the remaining operations in the numerator: $$\frac{221}{5 \cdot 6-3(5)-2}$$

Step 5: Solve the multiplication and division operations in the denominator

Next, we will solve the multiplication and division operations in the denominator: $$\frac{221}{30-15-2}$$

Step 6: Solve the addition and subtraction operations in the denominator

Finally, we will solve the addition and subtraction operations in the denominator: $$\frac{221}{13}$$ The result of the given expression is $$\frac{221}{13}$$.