Question

Use the image to answer the question.

A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. An open circle is marked on the number line at 4.5. A line is drawn from the circle toward negative 10 with an arrow at the end.

Willow solved an inequality and graphed the solution on the number line. Which of the following inequalities did she solve?

(1 point)
Responses

x+1.25≤5.75
x plus 1.25 less-than-or-equal-to 5.75

x+212<212
x plus 2 Start Fraction 1 over 2 End Fraction less than 2 Start Fraction 1 over 2 End Fraction

x−213<216
x minus 2 Start Fraction 1 over 3 End Fraction less than 2 Start Fraction 1 over 6 End Fraction

x−1.5≤3

Answer 1

The open circle at 4.5 with the arrow left means x < 4.5.

Check each:
- x + 1.25 ≤ 5.75 → x ≤ 4.5 (closed) — no.
- x + 2 1/2 < 2 1/2 → x < 0 — no.
- x − 2 1/3 < 2 1/6 → x < 2 1/6 + 2 1/3 = 13/6 + 14/6 = 27/6 = 4.5 → x < 4.5 — matches.
- x − 1.5 ≤ 3 → x ≤ 4.5 (closed) — no.

So the correct inequality is x − 2 1/3 < 2 1/6.