Solve the inequality and graph the solution.

Question

54≥27(v–4)
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 \(54 \geq 27(v - 4)\), we first isolate the variable \(v\).

1. Start by distributing \(27\) on the right side: \[ 54 \geq 27v - 108 \]

2. Next, add \(108\) to both sides: \[ 54 + 108 \geq 27v \] \[ 162 \geq 27v \]

3. Now, divide both sides by \(27\): \[ \frac{162}{27} \geq v \] \[ 6 \geq v \] or equivalently, \[ v \leq 6 \]

The solution to the inequality is \(v \leq 6\).

Graphing the Solution:

• We will create a number line to graph the solution.

Step 1: Identify the endpoints.

• The endpoint here is \(6\).

Step 2: Decide on whether to use a closed or open endpoint.

• Since the inequality is "less than or equal to" (\( \leq \)), we use a closed dot at \(6\).

Step 3: Determine the direction of the ray.

• The solution indicates that \(v\) can be any number up to and including \(6\); therefore, the graph will extend to the left from \(6\).

Final Graph:

We will plot it on a number line:

<---•====================>
     6

• The closed dot (•) at \(6\) indicates that \(6\) is included in the solution, and the shading (or line) to the left indicates that all values less than \(6\) are part of the solution.