Solve the inequality and graph the solution.

Question

p/2+5>4

Answer 1

To solve the inequality \( \frac{p}{2} + 5 > 4 \), follow these steps:

1. Subtract 5 from both sides: \[ \frac{p}{2} > 4 - 5 \] \[ \frac{p}{2} > -1 \]

2. Multiply both sides by 2 (note that multiplying or dividing by a positive number does not change the inequality): \[ p > -2 \]

The solution to the inequality is \( p > -2 \).

Graphing the solution:

To graph \( p > -2 \):

• Draw a number line.
• Mark the point at -2.
• Since it's a strict inequality (greater than, not greater than or equal to), draw an open circle at -2 to indicate that -2 is not included in the solution.
• Shade to the right of -2 to show all numbers greater than -2.

Here’s a simple representation of the graph:

<---o========================>
      -2

In this graph:

• The open circle (o) at -2 indicates that -2 is not part of the solution.
• The shaded line to the right indicates all values greater than -2 are included in the solution.