Question

Ellen drew a graph showing the solution to an inequality.

A number line going from negative 1.25 to positive 0.75. An open circle is at negative 0.75. Everything to the left of the circle is shaded.

Which inequality does Ellen’s graph show the solution to?
3.25 less-than 2.5 + r
3.25 greater-than 2.5 + r
Negative 3.25 less-than negative 2.5 + r
Negative 3.25 greater-than negative 2.5 + r

Answer 1

Solve each inequality for r and match it to r < -0.75 (open circle at -0.75, shaded left).

1) 3.25 < 2.5 + r → 0.75 < r (r > 0.75) — no.
2) 3.25 > 2.5 + r → 0.75 > r (r < 0.75) — no.
3) −3.25 < −2.5 + r → −0.75 < r (r > −0.75) — no.
4) −3.25 > −2.5 + r → −0.75 > r (r < −0.75) — yes.

So the correct inequality is: −3.25 > −2.5 + r.