Question

Write and graph an inequality that represents the numbers that are not solutions of each inequality.

a.

`x + 8 < 14`
b.

`x - 12 \geqslant 5.7`

Answer 1

The inequalities representing numbers that are not solutions are x + 8 ≥ 14 and x - 12 < 5.7. The first is graphed with a closed circle at 6 and shading to the right, the second with an open circle at 17.7 and shading to the left.

Step-by-step explanation:

To write an inequality representing numbers that are not solutions of the given inequalities, we need to consider the opposite of the original conditions:

1. For the inequality x + 8 < 14, the numbers that are not solutions will satisfy the inequality x + 8 ≥ 14. To graph this, we represent everything on the number line to the right of 6 (since 6 is the point where x+8 equals 14), including 6 itself, indicating a closed circle at 6 and shading to the right.
2. For the inequality x - 12 ≥ 5.7, the numbers that are not solutions will satisfy the inequality x - 12 < 5.7. The graph consists of a number line with an open circle at 17.7 (since 17.7 is the point where x-12 equals 5.7) and shading to the left.

Answer 2

a.) x + 8 < 14
-8 -8
x < 6
b.) x - 12 >/= 5.7
+12 +12
x >/= 17.7