Question

Explain why the solution set of the inequality |x|<5 is the intersection of two sets, while the solution set of the inequality |x|>5 is the union of two sets.The solution of |x|<5 is the set of numbers that makes either of two inequalities true. The solution set of |x|>5 is the set of numbers that makes both of two inequalities true. The solution of |x|<5 is the set of numbers between −5 and 5. The solution set of |x|>5 is the set of numbers greater than 5. The solution of |x|<5 is the set of numbers that makes both of two inequalities true. The solution of |x|>5 is the set of numbers that makes either of two inequalities true. The solution of |x|<5 is the set of numbers less than −5. The solution of |x|>5 is the set of numbers between −5 and 5.

Answer 1

Answer:

The region of the $|x|$ is the common area between -5 and 5.

But there is no common area for the solution of $|x|>5$.

Step-by-step explanation:

Given two modulus functions:

$1.\ |x|5$

Let us have a look at the definition of modulus function first:

$|x|=\left \{ {-{x}\ if\ x0} \right.$

Now, solving the above given modulus functions one by one using the definition of modulus function.

Solution 1 :

$\pm x$

Kindly refer to the attached diagram for solution.

The area shaded in the green color shows the solution for this equation.

Solution 2 :

$\pm x >5\\\Rightarrow x>5, -x>5\\OR\\\Rightarrow x>5, x$

Kindly refer to the attached diagram for solution.

The area shaded in the blue color shows the solution for this equation.

We can clearly observe that the region of the first equation is the common area between -5 and 5.

But there is no common area for the solution of the second equation.

Therefore, solution of $|x|$ has intersection and

solution of $|x|>5$ has union.