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IM Alg2.3.10 Lesson: A New Kind of Number

Jada was helping her cousin with his math homework. He was supposed to solve the equation . He said, “If I subtract 8 from both sides, I get . This doesn’t make sense. You can’t subtract a bigger number from a smaller number. If I have 5 grapes, I can’t eat 8 of them!” What do you think Jada could say to her cousin to help him understand why  actually does make sense?

Numbers on the number line are often called real numbers. The equation  has 2 real solutions. How can you see this on the graph of ?

Draw points on this real number line to represent these 2 solutions.

How many real solutions does  have? Explain how you can see this on the graph of .

Draw the solution(s) on a real number line.

How many real solutions does  have? Explain how you can see this on the graph of .

Draw the solution(s) on a real number line.

On the real number line:

  • Draw an arrow starting at 0 that represents 3.
  • Draw an arrow starting at 0 that represents -5.
This diagram shows an arrow that represents .

Draw an arrow starting at 0 that represents . Draw an arrow starting at 0 that represents . Draw an arrow starting at 0 that represents 

The absolute value of a real number is the length of the arrow that represents it.

What is the relationship between the absolute value of a real number and the absolute value of the square of that number?

If we want  and its square to have this same relationship, then what should the absolute value of  be?

What should the absolute value of   be?