Question

Describe the graph of this inequality: 2x + 3 > 9

Answer 1

Open circle at 3 going to the right.

Explanation:

Let’s look at this.

first, let’s simplify the inequality. 2x +3-3>9-3

2x>6

x>3

since this is just a greater than or less than, it will be an open circle.

now that we have established that, we can see that x is BIGGER than 3. In that case, it will be an open circle at 3 going to the right.

Answer 2

The graph of the inequality is a circle with an arrow pointing to the right and a closed circle at -3 with an arrow pointing to the left.

The inequality can be solved by moving all like terms to one side, and then dividing both sides by the coefficient of the x-term. This gives:

\begin{align*}2x + 3 &> 9 \2x &= 6\ x &= 3\end{align*}

We can then plot the points (-3, 0) and (3, 0). Since the inequality does not contain an equal sign, the solution is not the line itself, but the half-plane that contains 3, but not -3. This is represented by an open circle at 3 and a closed circle at -3.

The arrow pointing to the right indicates that the solution set is all the x-values greater than 3. We can also see that this solution set is all x-values that satisfy the inequality x > 3.