Question

the product of a number and -3, increased by 8, is 20.

Explanation:

Step1: Define the variable

Let the number be \( x \). The product of the number and -3 is \( -3x \).

Step2: Translate the sentence into an equation

"Increased by 8" means we add 8 to \( -3x \), and "is 20" means this expression equals 20. So the equation is \( -3x + 8 = 20 \).

Step3: Solve the equation for \( x \)

Subtract 8 from both sides: \( -3x + 8 - 8 = 20 - 8 \), which simplifies to \( -3x = 12 \).
Divide both sides by -3: \( \frac{-3x}{-3} = \frac{12}{-3} \), so \( x = - 4 \).

Answer:

The number is \(-4\)