Problem 58 - Elementary Algebra

Question

Determine whether the statements for the following problems are true or false. $$2[6(1+4)-8]>3(11+6)$$

Step-by-Step Solution

Answer

Answer: False

Step 1: Apply the order of operations (PEMDAS) to simplify the expressions on both sides of the inequality:

To simplify the expressions, we need to follow the order of operations: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

Step 2: Simplify the expressions inside the parentheses:

Start with simplifying the expression within the parentheses: $$6(1+4)$$ $$6(5)$$ Now the inequality looks like this: $$2[6(5)-8]>3(11+6)$$

Step 3: Perform the multiplication and division operations:

Multiply 6 by 5 and perform the multiplication on the left side of the inequality: $$2[30-8]>3(11+6)$$ Simplify further: $$2[22]>3(11+6)$$

Step 4: Simplify the expressions inside the remaining parentheses:

Add 11 and 6 on the right side of the inequality: $$2[22]>3(17)$$

Step 5: Perform the remaining multiplication operations:

Multiply 2 by 22 and 3 by 17 to get: $$44>51$$

Step 6: Compare the results and determine if the inequality is true or false:

Since 44 is not greater than 51, the inequality is false.