Question

Find the solution of the linear inequality and express the solution set in set notation and interval notation. Graph the solution set on the real number line.

x + 7 < 8
A) (-[infinity], 1)
B) (-[infinity], -15)
C) (-[infinity], -8)
D) (-[infinity], -6)

Answer 1

The solution of the linear inequality x + 7 < 8 is x < 1, which in set notation is x < 1 and in interval notation is (-∞, 1). Option A is correct and to visualize it, an open circle is placed at 1 on a real number line extending from negative infinity.

Step-by-step explanation:

To find the solution of the linear inequality x + 7 < 8, we subtract 7 from both sides to isolate x:

x + 7 - 7 < 8 - 7

x < 1

The solution set in set notation is x , and in interval notation, it is (-∞, 1). The correct choice is A) (-∞, 1).

To graph this on the real number line, we draw a line starting from negative infinity up to, but not including, 1. At 1, we place an open circle to indicate that 1 is not included in the solution set.