Solve and graph the solution set on a number line :
`5x+4 gt 8x -11, x in `

Answer

To solve the inequality \(5x + 4 > 8x - 11\) and graph the solution set on a number line, we can follow these steps:

### Step 1: Rewrite the inequality
Start with the given inequality:
\[ 5x + 4 > 8x - 11 \]

### Step 2: Move all terms involving \(x\) to one side
To isolate \(x\), we can first add \(11\) to both sides:
\[ 5x + 4 + 11 > 8x - 11 + 11 \]
This simplifies to:
\[ 5x + 15 > 8x \]

### Step 3: Move the \(x\) terms to one side
Next, subtract \(5x\) from both sides:
\[ 5x + 15 - 5x > 8x - 5x \]
This simplifies to:
\[ 15 > 3x \]
or equivalently:
\[ 3x < 15 \]

### Step 4: Solve for \(x\)
Now, divide both sides by \(3\):
\[ \frac{3x}{3} < \frac{15}{3} \]
This simplifies to:
\[ x < 5 \]

### Step 5: Graph the solution on a number line
To graph \(x < 5\):
1. Draw a number line.
2. Mark the point \(5\) on the number line.
3. Since \(5\) is not included in the solution (as indicated by the "<" sign), draw an open circle at \(5\).
4. Shade the line to the left of \(5\) to indicate all numbers less than \(5\).

### Final Solution
The solution to the inequality \(5x + 4 > 8x - 11\) is:
\[ x < 5 \]