Question

1. the product of a number and 4 is at least -12.

inequality:
solution:

Explanation:

Step1: Define the variable

Let the number be \( x \). The product of the number and 4 is \( 4x \). "At least" means greater than or equal to, so the inequality is \( 4x \geq - 12 \).

Step2: Solve the inequality

To solve for \( x \), divide both sides of the inequality \( 4x \geq - 12 \) by 4. When dividing an inequality by a positive number, the direction of the inequality sign remains the same. So we have \( \frac{4x}{4}\geq\frac{-12}{4} \), which simplifies to \( x\geq - 3 \).

Answer:

Inequality: \( 4x \geq - 12 \)
Solution: \( x\geq - 3 \)