Question

question
solve the inequality and graph the solution on the line provided.
-2 + 3x ≤ -17
answer attempt 1 out of 3
inequality notation:
number line:

Explanation:

Step1: Add 2 to both sides

To isolate the term with \( x \), we add 2 to both sides of the inequality \( -2 + 3x \leq -17 \). This gives \( -2 + 2 + 3x \leq -17 + 2 \), which simplifies to \( 3x \leq -15 \).

Step2: Divide by 3

Next, we divide both sides of the inequality \( 3x \leq -15 \) by 3. Since 3 is positive, the direction of the inequality sign remains the same. So, \( \frac{3x}{3} \leq \frac{-15}{3} \), which simplifies to \( x \leq -5 \).

Answer:

Inequality Notation: \( x \leq -5 \)
For the number line: We would place a closed circle at -5 (because the inequality is "less than or equal to") and shade to the left of -5 to represent all values of \( x \) that satisfy the inequality.