You just found three rules that give you an output of 12 when the input is 6. Now, here are some more input-output pairs in the table. Which rule would make all of these input-output pairs true?

Question

input
Input Output Arrow
rule
Input Output Arrow
ouput

Input Output
6 12
8 12
13 12
9 12

Subtract 3, then multiply by 4.

Write 12.

Multiply by 2.

Answer 1

To determine which rule would yield an output of 12 for all the given inputs (6, 8, 13, and 9), we need to evaluate each proposed rule:

1. Subtract 3, then multiply by 4:

   • For input 6: (6 - 3) * 4 = 3 * 4 = 12
   • For input 8: (8 - 3) * 4 = 5 * 4 = 20
   • For input 13: (13 - 3) * 4 = 10 * 4 = 40
   • For input 9: (9 - 3) * 4 = 6 * 4 = 24

   This rule does not produce an output of 12 for all inputs.

2. Write 12:

   • For all inputs (6, 8, 13, and 9), the output is 12. An input of any value will always yield an output of 12.

   This rule produces an output of 12 for all values.

3. Multiply by 2:

   • For input 6: 6 * 2 = 12
   • For input 8: 8 * 2 = 16
   • For input 13: 13 * 2 = 26
   • For input 9: 9 * 2 = 18

   This rule does not produce an output of 12 for all inputs.

After evaluating all the rules, the rule that would make all of the input-output pairs true is "Write 12."