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.

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b