write and solve an inequalit for the following. Flix Theater has a reduced ticket price for children who are at least two years old but less than 13 years old. The same price is given to seniors who are at least 65 years old. Also model these ranges on a number line.

To write and solve an inequality that represents the age range for children and seniors and model it on a number line, we need to establish the minimum and maximum values for each group.

For children, we know that they must be at least 2 years old (inclusive), but less than 13 years old (exclusive). So we can write the inequality as:
2 ≤ x < 13

Here, "x" represents the age of a child.

For seniors, we know that they must be at least 65 years old (inclusive). So we can write the inequality as:
x ≥ 65

Here, "x" represents the age of a senior.

To model these ranges on a number line, we can draw a horizontal line and place a closed dot at the point for 2 (to represent the inclusive condition) and an open dot at 13 (to represent the exclusive condition) to indicate the age range for children. Then, we can draw another closed dot at the point for 65 (to represent the inclusive condition) to indicate the age range for seniors.

Here's how it would look on a number line:

0 10 20 30 ... 60 70 ...
┼-------------┼--------------┼--------------┼--------------┼--------------┼--------------┼---...
2 13 65

The shaded area between the closed dot at 2 and open dot at 13 represents the age range for children (2 ≤ x < 13). The shaded area to the right of the closed dot at 65 represents the age range for seniors (x ≥ 65).

To represent the age ranges on a number line, we can use inequalities.

Let's assume that x represents the age of a person.

For children, the age range is from 2 years old (inclusive) to less than 13 years old (exclusive). This can be represented as:

2 ≤ x < 13

For seniors, the age range is at least 65 years old or greater. This can be represented as:

x ≥ 65

To model these ranges on a number line, we can draw a number line and mark the interval for each age range.

On the number line, mark the points 2 and 13 with a closed circle at 2 and an open circle at 13 to represent the range for children. Connect the two points with a solid line.

Next, mark the point 65 with a closed circle to represent the age for seniors. Draw an arrow to the right to show that it continues indefinitely in that direction.

2-------------------13
o\________________

---------------->

This representation shows that children between the ages of 2 and 13 (inclusive of 2 and exclusive of 13) are eligible for reduced tickets, while seniors aged 65 and older are also eligible for the same reduced ticket price.

13 > children >= 2

seniors >= 65

discounted tickets are in the range "[2,13) U [65,INFINITY]" in terms of "years old"

So on a number line, you would put a dot at 2, a circle at 13, and connect the two with a line. You would also put a dot at 65 and draw a line to the right with an arrow.