Which sentence can represent the inequality 2.4(6.2-x)> – 4.5
A.Two and four tenths times six and two tenths minus a number is larger than negative four and five tenths.
B.Two and four tenths multiplied by the difference of six and two tenths and a number is more than negative four and five tenths.
C.The difference of six and two tenths and a number multiplied by two and four tenths is not less than negative four and five tenths
D.The product of six and two tenths minus a number and two and four tenths is at minimum negative four and five tenths
The Correct Answer and Explanation is :
The correct sentence that represents the inequality (2.4(6.2 – x) > -4.5) is:
B. Two and four tenths multiplied by the difference of six and two tenths and a number is more than negative four and five tenths.
Explanation:
Let’s break down the inequality:
- (2.4(6.2 – x)): The expression means “two and four tenths” (which is 2.4) is multiplied by the difference between 6.2 and some number, represented by (x). This multiplication represents the distributive property, where you multiply the 2.4 by both 6.2 and ( -x ).
- In the context of language, this is best described by saying “two and four tenths multiplied by the difference of six and two tenths and a number.”
- The symbol (>) means “is more than” or “greater than.” This represents an inequality, showing that the left-hand side is larger than the right-hand side.
- (-4.5): This is “negative four and five tenths,” which is straightforward and means the expression on the left should be greater than (-4.5).
Why B is Correct:
The sentence in option B accurately represents the multiplication involved in the expression, as well as the subtraction within the parentheses. “Two and four tenths multiplied by the difference” precisely describes how the multiplication is happening after subtracting the number (x) from 6.2. The phrase “is more than negative four and five tenths” matches the (>) symbol in the inequality, showing the correct relationship between the two sides of the equation.
Why the Other Options are Incorrect:
- A doesn’t make it clear that the entire quantity (6.2 – x) is being multiplied by 2.4.
- C incorrectly introduces the phrase “is not less than,” which means (\geq) (greater than or equal to), but the inequality symbol is strictly (>) (greater than).
- D uses the phrase “at minimum,” implying the use of (\geq) rather than (>).
Thus, B is the most accurate description of the inequality.