Answer :
Sure! Let's break down the problem step-by-step:
The sentence we have is: "The sum of negative 3.2 and 1.5 times a number is a maximum of 8.6."
To express this as an inequality, follow these steps:
1. Identify the Components:
- Negative 3.2 is written as [tex]\(-3.2\)[/tex].
- "1.5 times a number" can be written as [tex]\(1.5 \times n\)[/tex], where [tex]\(n\)[/tex] represents the unknown number.
2. Translate the Sentence into a Mathematical Expression:
- The sentence says "the sum of negative 3.2 and 1.5 times a number." So, add [tex]\(-3.2\)[/tex] and [tex]\(1.5n\)[/tex]. This gives us the expression [tex]\(-3.2 + 1.5n\)[/tex].
3. Set Up the Inequality:
- The phrase "is a maximum of 8.6" means that the expression [tex]\(-3.2 + 1.5n\)[/tex] can be at most 8.6. In mathematical terms, this means it is less than or equal to 8.6.
- Therefore, we write the inequality as: [tex]\(-3.2 + 1.5n \leq 8.6\)[/tex].
So the inequality that represents the sentence is:
\-3.2 + 1.5n ≤ 8.6
The sentence we have is: "The sum of negative 3.2 and 1.5 times a number is a maximum of 8.6."
To express this as an inequality, follow these steps:
1. Identify the Components:
- Negative 3.2 is written as [tex]\(-3.2\)[/tex].
- "1.5 times a number" can be written as [tex]\(1.5 \times n\)[/tex], where [tex]\(n\)[/tex] represents the unknown number.
2. Translate the Sentence into a Mathematical Expression:
- The sentence says "the sum of negative 3.2 and 1.5 times a number." So, add [tex]\(-3.2\)[/tex] and [tex]\(1.5n\)[/tex]. This gives us the expression [tex]\(-3.2 + 1.5n\)[/tex].
3. Set Up the Inequality:
- The phrase "is a maximum of 8.6" means that the expression [tex]\(-3.2 + 1.5n\)[/tex] can be at most 8.6. In mathematical terms, this means it is less than or equal to 8.6.
- Therefore, we write the inequality as: [tex]\(-3.2 + 1.5n \leq 8.6\)[/tex].
So the inequality that represents the sentence is:
\-3.2 + 1.5n ≤ 8.6
