Question

solve for x and graph the solution on the number line below. 2 < x + 5

Explanation:

Step1: Subtract 5 from both sides

To solve for \( x \) in the inequality \( 2 < x + 5 \), we subtract 5 from both sides of the inequality. This is based on the property of inequalities that allows us to add or subtract the same number from both sides without changing the direction of the inequality.
\[
2 - 5 < x + 5 - 5
\]

Step2: Simplify both sides

Simplifying the left - hand side \( 2-5=-3 \) and the right - hand side \( x + 5-5=x \). So we get:
\[
-3 < x
\]
Which can also be written as \( x > - 3 \).

To graph this solution on the number line:

1. Draw a number line.
2. Locate the point \( - 3 \) on the number line.
3. Since \( x\) is greater than \( - 3 \) (not greater than or equal to), we draw an open circle at \( - 3 \) (an open circle indicates that \( - 3 \) is not included in the solution set).
4. Then, we draw an arrow starting from the open circle at \( - 3 \) and pointing to the right (towards the positive infinity) to represent all the numbers greater than \( - 3 \).

Answer:

The solution to the inequality \( 2 < x + 5 \) is \( x > - 3 \). For the graph, there is an open circle at \( - 3 \) on the number line and an arrow pointing to the right from \( - 3 \).