Question

solve for x and graph the solution on the number line below. 3 < x - 5. answer. inequality notation: blank. number line: number line from -12 to 12.

Explanation:

Step1: Solve the inequality

To solve \( 3 < x - 5 \), we add 5 to both sides of the inequality.
Adding 5 to both sides gives \( 3 + 5 < x - 5 + 5 \), which simplifies to \( 8 < x \) or \( x > 8 \).

Step2: Graph the solution (description)

On the number line, we have an open circle at 8 (since the inequality is strict, \( > \), not \( \geq \)) and an arrow pointing to the right (indicating all numbers greater than 8).

Answer:

Inequality Notation: \( x > 8 \)
(For the number line: Place an open dot at 8 and draw an arrow to the right.)