Question

Which of the following inequalities would be graphed with an open circle?

Answer 1

3(x - 2) < 18 and h + 6 > -3h + 12 would be graphed with an open circle.

Open circle is a term used for numbers that are less than (<) or greater than (>). On the other hand, Closed circle is used for numbers that are less than or equal to (≤ ) and greater than or equal to (≥).

Here, we are given four inequalities, let us check them one by one-

A. h + 6 > -3h + 12

⇒ 4h > 6

or h > 3/2

Here, we see that there is no equality sign, this means that 3/2 won't be included and hence h + 6 > -3h + 12 would be an open circle inequality.

B. 7 ≥ d/3

⇒ d ≤ 21

Here, we can clearly see the equality sign which means that 21 will be included. Hence, 7 ≥ d/3 would not be graphed with an open circle.

C. 3(x - 2) < 18

x - 2 < 6

x < 8

Here, we see that there is no equality sign, this means that 8 won't be included and hence 3(x - 2) < 18 would be graphed with an open circle.

D. 2y ≤ 14

y ≤ 7

Here, we can clearly see the equality sign which means that 7 will be included. Hence, 2y ≤ 14 would not be graphed with an open circle.

Thus, 3(x - 2) < 18 and h + 6 > -3h + 12 would be graphed with an open circle.

Learn more about inequalities here-

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