Question

Suppose we want to choose a value of x at least 5 units away from 14.A) Think about some values of x that meet this constraint.B) Write an inequality that represents all values of x that meet this constraint. Hint. no answer givenC) On the number line below, represent all values of x that meet this constraint. Clear All Draw: Line segments and raysClosed dotOpen dot

Answer 1

Answer:

(a) [9, 19]

(b)  $9 \leq x \leq 19$

(c)See attachment

Step-by-step explanation:

We want to choose a value of x at least 5 units away from 14.

(a)Now, 14-5=9 and 14+5=19

The possible values of x ranges is in the closed interval [9,19]

(b) Since x is at least 5 units away from 14, we have:

$|14-x|\leq5$

Solving the absolute inequality

$-5 \leq 14-x \leq 5\\ In -5 \leq 14-x\\ x \leq 14+5\\x \leq 19\\\\ In 14-x \leq 5\\ 14-5 \leq x\\9 \leq x\\ Therefore,an inequality that represents all values of x that meet this constraint is: \\9 \leq x \leq 19$

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

Answer 2

Inequalities are used to represent unequal expressions.

• The inequality that represents the scenario is $\mathbf{|x-14| \ge 5}$
• Some possible values of x are: 5 and 20

Represent the value with x.

A value that is at least 5 from 14 can take any of the following forms:

$\mathbf{14 -x \ge 5}$

$\mathbf{x-14 \ge 5}$

The inequalities can be combined as:

$\mathbf{|x-14| \ge 5}$

The values of x are solved as follows:

$\mathbf{14 -x \ge 5}$

$\mathbf{14 - 5 \ge x}$

$\mathbf{9\ge x}$

Rewrite as:

$\mathbf{x \le 9}$

Similarly, we have:

$\mathbf{x-14 \ge 5}$

$\mathbf{x \ge 14 + 5}$

$\mathbf{x \ge 19}$

So, we have:

$\mathbf{x \le 9}$ or $\mathbf{x \ge 19}$

This can be combined as:

$\mathbf{9 \ge x \ u\ x \ge 19}$

Some possible values of x are: 5 and 20

Read more about inequalities at:

https://brainly.com/question/1930605