Problem 55 - Elementary Algebra

Question

Determine whether the statements for the following problems are true or false. $$5(4+2 \cdot 10) \geq 110$$

Step-by-Step Solution

Answer

Answer: The given statement is true.

Step 1: Rewrite the inequality

Let's rewrite the inequality as an equation to make the comparison easier: $$5(4+2 \cdot 10) \geq 110$$

Step 2: Apply the order of operations (PEMDAS) on the left side of the inequality

The order of operations is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). So, the first thing we need to do is solve inside the parentheses: $$5(4+2 \cdot 10) = 5(4+20)$$

Step 3: Continue applying the order of operations

Now, we will complete the addition operation inside the parentheses: $$5(4+20) = 5(24)$$

Step 4: Perform the final calculation

Lastly, perform the multiplication operation on the left side of the inequality: $$5(24) = 120$$

Step 5: Compare the results on both sides of the inequality

Let's compare our result with the number on the right side of the inequality: $$120 \geq 110$$ Since 120 is greater than or equal to 110, the given statement is True.