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Chapter 2: Problem 58

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

Short Answer

Expert verified
Answer: False

Step by step solution

01

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).
02

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: $$2[6(5)-8]>3(11+6)$$
03

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: $$2[22]>3(11+6)$$
04

Simplify the expressions inside the remaining parentheses:

Add 11 and 6 on the right side of the inequality: $$2[22]>3(17)$$
05

Perform the remaining multiplication operations:

Multiply 2 by 22 and 3 by 17 to get: $$44>51$$
06

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

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

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