Question

graph the solution to the inequality on the number line.

\\|w - 2| \ge 7\\

Explanation:

Set up the compound inequality

Using the Absolute Value and Compound Inequalities knowledge points

$$ w - 2 \le -7 \quad \text{or} \quad w - 2 \ge 7 $$

Solve the first inequality

Using the Compound Inequalities knowledge point

$$
LATEXBLOCK0
$$

Solve the second inequality

Using the Compound Inequalities knowledge point

$$
LATEXBLOCK1
$$

Combine the solutions

Using the Compound Inequalities knowledge point

$$ w \le -5 \quad \text{or} \quad w \ge 9 $$

Graph on the number line

Using the Number Line Graphing knowledge point

• Solid circle at \(w = -5\) with a ray pointing to the left.
• Solid circle at \(w = 9\) with a ray pointing to the right.

Answer:

The solution to the inequality is \(w \le -5\) or \(w \ge 9\).

To graph this on the number line:

• Place a closed (solid) circle at \(-5\) and draw an arrow pointing to the left.
• Place a closed (solid) circle at \(9\) and draw an arrow pointing to the right.