To solve the inequality 2x + 63 < x - 4:
1. Subtract x from both sides to isolate x:
2x + 63 < x - 4
2x - x + 63 < x - x - 4
x + 63 < -4
2. Subtract 63 from both sides to continue isolating x:
x + 63 - 63 < -4 - 63
x < -67
Therefore, the solution to the inequality 2x + 63 < x - 4 is x < -67. This means that any real number less than -67 would satisfy the inequality.
Now, let's sketch the solution on the real number line:
-67 would be represented by an open circle on -67 on the number line, indicating that -67 is not included in the solution set. To the left of -67 would be all the real numbers that are less than -67.
Remember to verify this solution graphically using a graphing utility if needed.
