Solve the inequality and graph the solution.

Question

2f+5>13

Answer 1

To solve the inequality \(2f + 5 > 13\), follow these steps:

1. Subtract 5 from both sides to isolate the term with \(f\): \[ 2f + 5 - 5 > 13 - 5 \] This simplifies to: \[ 2f > 8 \]

2. Next, divide both sides by 2 to solve for \(f\): \[ f > \frac{8}{2} \] This simplifies to: \[ f > 4 \]

The solution to the inequality is \(f > 4\).

Graphing the Solution

To graph the solution on a number line:

1. Draw a horizontal line to represent the number line.
2. Locate the point \(4\) on the number line.
3. Since the inequality is strict (\(>\)), use an open circle at \(4\) to indicate that \(4\) is not included in the solution (i.e., \(f\) cannot equal \(4\)).
4. Shade to the right of \(4\) to represent all numbers greater than \(4\).

The final graph looks like this:

<---|----|----|----|----|----|----|----|----|--->
         3    4    5    6    7

          (-----------------------)

Here, the open circle at \(4\) signifies that \(f\) is greater than \(4\), and the shading indicates that all numbers greater than \(4\) are included in the solution.