Beginning Activity 1: Integer Solutions for Linear Equations in One Variable

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Beginning Activity Beginning Activity 1: Integer Solutions for Linear Equations in One Variable
A4 US

1.

Does the linear equation $6 x = 42$ have a solution that is an integer? Explain.

2.

Does the linear equation $7 x = - 21$ have a solution that is an integer? Explain.

3.

Does the linear equation $4 x = 9$ have a solution that is an integer? Explain.

4.

Does the linear equation $- 3 x = 20$ have a solution that is an integer? Explain.

5.

Prove the following theorem:

Theorem 8.20.

Let $a, b \in Z$ with $a \neq 0 .$

If $a$ divides $b,$ then the equation $a x = b$ has exactly one solution that is an integer.
If $a$ does not divide $b,$ then the equation $a x = b$ has no solution that is an integer.