Solve the inequality and graph the solution.

Question

5(y–2)<10
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality \(5(y - 2) < 10\), we will follow these steps:

1. Distribute and simplify: \[ 5y - 10 < 10 \]

2. Add 10 to both sides: \[ 5y < 20 \]

3. Divide by 5: \[ y < 4 \]

The solution to the inequality is \(y < 4\).

Graphing the solution:

• Endpoints: The endpoint here is \(y = 4\). We will plot the point \(4\) on the number line.
• Open vs. closed endpoint: Since \(y\) is less than \(4\) (not including \(4\)), we will use an open circle at \(4\).
• Direction: The inequality \(y < 4\) indicates all values less than \(4\), so we shade to the left of \(4\).

Graph representation:

On a number line:

1. Draw an empty circle at \(4\) (open endpoint).
2. Shade the line to the left of \(4\).

Here’s a simple representation:

-----o========================>
     4

The open circle at \(4\) indicates that \(4\) is not included in the solution set, and the shaded part indicates all values less than \(4\) are included.