Solve the inequality and graph the solution.

Question

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12<4(s–1)
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 \(-12 < 4(s - 1)\), we'll follow these steps:

1. Distribute the \(4\) on the right side: \[ -12 < 4s - 4 \]

2. Add \(4\) to both sides of the inequality: \[ -12 + 4 < 4s \] \[ -8 < 4s \]

3. Divide both sides by \(4\): \[ -2 < s \] This can also be rewritten as: \[ s > -2 \]

Now, let's express the solution set in interval notation:

• The solution is \(s \in (-2, \infty)\).

Graphing the solution:

1. Endpoints: The endpoint is \(-2\). Since \(s > -2\), we will make this endpoint open (not included).

2. Graph:

   • Draw a number line.
   • Place an open circle at \(-2\).
   • Shade to the right of \(-2\) extending to infinity.

Visual Representation:

Here's how you would represent it visually, though I cannot draw directly:

<---(-2)========>

• The paranthesis \(()\) around \(-2\) indicates that it is an open endpoint, meaning \(-2\) is not included in the solution set.
• The shading to the right indicates that all values greater than \(-2\) are included in the solution.