Question

1. -10 > \frac{x}{-1}3

Explanation:

Step1: Add 1 to both sides

To isolate the term with \( x \), we add 1 to both sides of the inequality \( -10 > \frac{x}{3}-1 \). This gives us \( -10 + 1>\frac{x}{3}-1 + 1 \), which simplifies to \( -9>\frac{x}{3} \).

Step2: Multiply both sides by 3

To solve for \( x \), we multiply both sides of the inequality \( -9>\frac{x}{3} \) by 3. Since 3 is a positive number, the direction of the inequality sign remains the same. So we have \( -9\times3>\frac{x}{3}\times3 \), which simplifies to \( -27 > x \) or \( x < -27 \).

Answer:

The solution to the inequality \( -10 > \frac{x}{3}-1 \) is \( x < -27 \). On the number line, we would draw an open circle at -27 (since the inequality is strict, \( x
eq - 27\)) and shade the region to the left of -27.