Question

How do I solve and graph this inequality?(2/3)x + 3 > 11

Answer 1

From the problem, we have the inequality :

$\frac{2}{3}x+3>11$

Substract both sides by 3

$\begin{gathered} \frac{2}{3}x+3-3>11-3 \\ \frac{2}{3}x>8 \end{gathered}$

Cross multiplication :

$\begin{gathered} 2x>8(3) \\ 2x>24 \end{gathered}$

Divide both sides by 2 :

$\begin{gathered} 2x>24 \\ x>12 \end{gathered}$

The solution is x > 12

To grahp this inequality, take note that the graph will be composed of a circle or endpoint and an arrow

If the inequality sign is < or >, the endpoint is an open circle.

If the inequality sign is ≤ or ≥, the endpoint is a closed or shaded circle.

Since the inequality symbol in the question is >, we will use an open circle.

The graph will look like this.

The endpoint is located at x = 12, and the direction is to the right since the sign is greater than ">"