Solve the inequality and graph the solution.

Question

19(m–2)–18>20
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 \( 19(m - 2) - 18 > 20 \), we will first simplify and solve for \( m \).

1. Start by distributing \( 19 \) in the expression: \[ 19m - 38 - 18 > 20 \]

2. Combine like terms: \[ 19m - 56 > 20 \]

3. Add \( 56 \) to both sides: \[ 19m > 76 \]

4. Divide both sides by \( 19 \): \[ m > 4 \]

Now we have the solution to the inequality: \( m > 4 \).

Graphing the solution:

1. Identify the endpoint, which is \( 4 \).

2. Since the solution is \( m > 4 \), we will use an open circle at \( 4 \) (indicating that \( 4 \) is not included in the solution).

3. Draw a ray extending to the right of \( 4 \) to represent all values greater than \( 4 \).

Summary of the graph:

• Open circle at \( 4 \)
• Ray starting just after \( 4 \) and continuing infinitely to the right.

Thus, the graphical representation of the solution \( m > 4 \) has the open circle and the ray extending to the right from \( 4 \).