Explain why not all solutions represented by inequation are always possible solutions in reality.

The answer is below!!

Step-by-step explanation:

Some inequalities do not have a solution. When two inequalities have parallel lines and the shaded areas do not overlap (i.e., the opposite areas are shaded), then the system has no solution. This means that there is no coordinate point that makes both inequalities true.

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Why aren't all solutions to an inequality possible in reality?

(TL;DR at the bottom, but the full explanation is better)

Let's answer this using an example.

The equation 2x + 5 > 10 can represent a lemonade stand's sales. What do each of the numbers represent in a real-life situation?

A solution for this equation would be x = -3:

2x + 5 > 10

2(-3) + 5 > 10

6 + 5 > 10

11 > 10 - True

Another solution is x = 11/3:

2x + 5 > 10

2(11/3) + 5 > 10

(22/3) + 5 > 10

(37/3) > 10

(36/3)+(1/3) > 10

12 and (1/3) > 10

These are solutions to our inequality from a mathematical standpoint but are both implausible in real life.

Assuming that reasonable would mean a full glass, -3 and (11/3) are possible answers, but can't be reasonably sold. -3 glasses of lemonade can't be sold, and neither can (11/3) of a glass of lemonade.

Therefore, these values create a situation where "not all solutions represented by inequation are always possible solutions in reality."

TL;DR:

    Not all solutions are possible because the value that makes the inequation true is not reasonable or feasible under realistic circumstances, such as a fraction value for people or a negative value for possession.

Step-by-step explanation:

y+2+8(y+7)

y+2+8y+56

9y+58