Question

1. if the sum of twice a number and -3 is multiplied by 4, the answer is 28. find the number.
2. is the product of 30 positive numbers and 33 negative numbers a positive number or a negative number?

Explanation:

Problem 2

Step1: Define the variable

Let the number be \( x \).

Step2: Translate the problem into an equation

Twice the number is \( 2x \), the sum of twice the number and \(-3\) is \( 2x - 3 \). Multiplying this by 4 gives \( 4(2x - 3) \), and this equals 28. So the equation is \( 4(2x - 3) = 28 \).

Step3: Solve the equation

First, divide both sides by 4: \( \frac{4(2x - 3)}{4}=\frac{28}{4} \), which simplifies to \( 2x - 3 = 7 \).
Then, add 3 to both sides: \( 2x - 3 + 3 = 7 + 3 \), so \( 2x = 10 \).
Finally, divide both sides by 2: \( \frac{2x}{2}=\frac{10}{2} \), so \( x = 5 \).

Step1: Recall the rule of multiplying positive and negative numbers

The product of an even number of negative numbers is positive, and the product of an odd number of negative numbers is negative. The product of positive numbers is always positive.

Step2: Analyze the number of negative numbers

Here, we have 33 negative numbers. Since 33 is an odd number, the product of 33 negative numbers is negative. The product of 30 positive numbers is positive.

Step3: Find the product of all numbers

The product of a positive number and a negative number is negative. So the product of 30 positive numbers and 33 negative numbers is negative.

Answer:

The number is \( 5 \).

Problem 3