Question

Apex Algebra 1

1.4.2 Using X to mark the spot

1. The sum of two rational numbers is rational, and the sum of a rational number and an irrational number is irrational. What about the sum of two irrational numbers? Decide whether the sum of two irrational numbers is always rational, always irrational, or either rational or irrational depending on the case. Share your answer with the group, and see if everyone agrees on the correct answer.

2. Come up with a word problem of your own and share it with the group. What reasonable values could you expect for the answer? What values would not be acceptable?

3. Write your own word problem that can be translated into the equation x + 4 = 10. What does the variable x represent in your problem? Share it with the rest of the group.

4. Write your own word problem and ask a classmate to translate it into an equation.

Answer 1

These are four questions and four answers

1) Question 1. Decide whether the sum of two irrational numbers is always rational, always irrational, or either rational or irrational depending on the case.

Answer: always irrational:

Explanation:

See some examples:

1) π + π = 2π

2) √2 + 8√2 = 9√2

3) 10∛7 + 15∛3 = 25∛7

There is not way to obtain a rational number when you add up two irrational numbers.

An irrational number is one that cannot be expressed as a fraction of two whole numbers. So, if you cannot express the sumands as fractions the result cannot be expressed as a fraction either.

2. Question 2: Come up with a word problem of your own and share it with the group. What reasonable values could you expect for the answer? What values would not be acceptable?

Answer: The sum of three consecutive numbers is 27.  Which is the least number.

Solution:

Call x the least number, then the other two numbers are x + 1 and x + 2.

And the sum of the three numbers is x + x + 1 + x + 2 = 27

Add like terms: 3x + 3 = 27

Subtract 3 from both sides of the equality: 3x + 3 - 3 = 27 - 3

=> 3x = 24

Divide both sides by  3 => (3x / 3) = 24 / 3

=> x = 8

Result: the least number is 8.

Verify: 8 + 9 + 10 = 27

3. Question 3.  Write your own word problem that can be translated into the equation x + 4 = 10. What does the variable x represent in your problem?

Answer:

The age of a kid in four years will be 10. How old is the kid now:

x represents the actual age.

x + 4 = 10.

4) Question 4. Write your own word problem and ask a classmate to translate it into an equation.

Answer: If you borrow $ 10 you will have 3 dolars more than the value of the entrance to the movie theather. If the value of the entrance is 25 dolars how much money you have now?

Translation:

name x the amount of money you have now.

x + 10 is the money after borrowing $ 10.

That equals the entrance price plus $ 10

=> x + 10 = 25 + 3

Solution:

x + 10 = 28
x + 10 - 10 = 28 - 10
x = 18.

Verify:

18 + 10 = 3 + 25
28 = 28 => check.