Question

10. The game instructions state that each player randomly chooses a number from 0 to 20. What would

happen if the choice were not random? Justify your answer. (2 points)
11. Alondra challenges you to play a math game. She says, "I am thinking of a whole number. If you
double my number and subtract 6, the result is less than 2 units away from 0. What number am I thinking
of?"
Write an absolute value inequality to solve this problem. Use x to represent Alondra's number. Explain
how you found the inequality. (4 points: 3 points for the inequality, 1 point for the explanation)
12. Solve your inequality. What is Alondra's number? How do you know? (4 points: 3 points for the
solution, 1 point for the explanation)

Answer 1

If the choice of numbers in the game were not random, it could potentially lead to unfair advantages. The absolute value inequality to represent Alondra's number is |2x - 6| < 2. Solving the inequality, Alondra's number can be any whole number between 2 and 4.

Step-by-step explanation:

If the choice of numbers in the game were not random, it could potentially lead to unfair advantages. For example, if one player knew that the other player always chose a certain number, they could strategically choose a number to ensure their own victory. Randomizing the number choices ensures a fair and unpredictable game.

To represent Alondra's number in the given math game, we can use the equation: |2x - 6| < 2. This inequality represents that the result of doubling Alondra's number and subtracting 6 should be less than 2 units away from 0.

To solve the inequality, we can isolate the absolute value by considering two cases: when the expression inside the absolute value is positive and when it is negative.

• Case 1: 2x - 6 < 2
  Solving this inequality, we find x < 4.
• Case 2: -(2x - 6) < 2
  Solving this inequality, we find x > 2.

Combining the solutions from both cases, we get 2 < x < 4. Therefore, Alondra's number can be any whole number between 2 and 4.

Learn more about Randomness in game choices, solving absolute value inequalities, finding a range of whole numbers