Question

which of the following shows the solution of the inequality x - 3 < -2?

Explanation:

Step1: Solve the inequality

To solve \( x - 3 < -2 \), add 3 to both sides of the inequality.
\( x - 3 + 3 < -2 + 3 \)
\( x < 1 \)

Step2: Analyze the number lines

• The first number line has a red dot at 2 and shades left, which is for \( x\leq2 \), not \( x < 1 \).
• The second number line has an open circle at 1 and shades left, which represents \( x < 1 \) (open circle means 1 is not included, shading left means all numbers less than 1).
• The third number line has an open circle at 0 and shades left, for \( x < 0 \), not correct.
• The fourth number line has an open circle at -1 and shades left, for \( x < -1 \), not correct.

Answer:

The number line with an open circle at 1 and shading to the left (the second number line from the left).