Question

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

Answer 1

From the problem, we have the inequality :

`(2)/(3)x+3>11`

Substract both sides by 3

`\begin{gathered} (2)/(3)x+3-3>11-3 \\ (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 ">"