Suppose we want to choose a value of x within 3 units of 11. [This means a value of x that is less than 3 units away from 11.] Think about some values of x that meet this constraint. Write an inequality that represents all values of x that meet this constraint. On the number line below, represent all values of x that meet this constraint.

The solution of the inequality is

According to the question, we need to choose a value of x within 3 units of 11. This can be represented by the inequality

The expression in modulus can be negative or positive:

For the positive inequality

For the negative inequality

Combining the inequalities

Hence the solution of the inequality is

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(a) [8, 14]

(b)  

(c)See attachment

Step-by-step explanation:

We want to choose a value of x within 3 units of 11.

(a)Now, 11-3=8 and 11+3=14

The possible values of x ranges is in the closed interval [8,14]

(b) Since x is within 3 units of 11., we have:

Solving the absolute inequality

(c)To draw the number line, we use a closed dot since we have the less than or equal to sign.