Graph the solution to the following inequality on the number line: 3(1 – x) < 2 (x + 4).

Inequalities are very important concepts in mathematics. They are used to represent feasible regions on the graph for specific parameters and calculate their range of values.

Answer: The simplified form of the given inequality is x > -1, which is represented on the number line.

Let's understand the solution in detail.

Explanation:

Given inequality: 3(1 – x) < 2 (x + 4)

Now, if we solve the inequality:

⇒ 3(1 – x) < 2 (x + 4)

⇒ 3 – 3x < 2x + 8

⇒ 3 - 8 < 2x + 3x

⇒ 5x > -5

⇒ x > -1

Now, we plot them on the cartesian plane below.

Hence, the simplified form of the given inequality is x > -1, which is represented on the number line.