To solve the inequality \( x + 7 > 1 \), follow these steps:
- Isolate \( x \): Subtract 7 from both sides of the inequality: \[ x + 7 - 7 > 1 - 7 \] \[ x > -6 \]
So, the solution to the inequality is \( x > -6 \).
Graphing the solution:
On a number line:
- Place an open circle at \(-6\) (indicating that \(-6\) is not included in the solution).
- Shade the line to the right of \(-6\) to indicate all values greater than \(-6\).
Checking the solution:
Choose a test point from the solution set (for example, \( x = 0 \)):
- Substitute \( x = 0 \) into the original inequality: \[ 0 + 7 > 1 \] \[ 7 > 1 \quad \text{(True)} \]
Now choose a test point not in the solution set (for example, \( x = -7 \)):
- Substitute \( x = -7 \) into the original inequality: \[ -7 + 7 > 1 \] \[ 0 > 1 \quad \text{(False)} \]
Since the inequality holds for points in the solution set and does not hold for points outside it, our solution \( x > -6 \) is confirmed.
Final answer:
\( x > -6 \)