A flow diagram has the rule: multiply the input by 5, then subtract 4. Complete the diagram by finding the missing input and output values.

• For input 11: $11 \times 5 - 4 = 55 - 4 = 51$
• For input 7: $7 \times 5 - 4 = 35 - 4 = 31$
• For input 2: $2 \times 5 - 4 = 10 - 4 = 6$
• For input 5: $5 \times 5 - 4 = 25 - 4 = 21$

To reverse the rule, we add 4 to the output, then divide by 5.
Reverse Rule: $(\text{Output} + 4) \div 5 = \text{Input}$

• For output 41: $(41 + 4) \div 5 = 45 \div 5 = 9$
• For output 26: $(26 + 4) \div 5 = 30 \div 5 = 6$

ii. What are the input values?
The input values are the numbers that go into the rule.
The input values are $\boxed{\text{11, 7, 9, 6, 2, 5}}$.

iii. What are the output values?
The output values are the numbers that come out of the rule.
The output values are $\boxed{\text{51, 31, 41, 26, 6, 21}}$.

iv. What is the rule?
The rule is given in the diagram.
The rule is $\boxed{\times 5 - 4}$.

v. Number sentences
Here are the number sentences for each input and its corresponding output:

• $11 \times 5 - 4 = 51$
• $7 \times 5 - 4 = 31$
• $9 \times 5 - 4 = 41$
• $6 \times 5 - 4 = 26$
• $2 \times 5 - 4 = 6$
• $5 \times 5 - 4 = 21$

vi. What will the output values be if the rule is $-4 \times 5$?
This rule means to multiply the input by 5, then subtract 4. We will use the original inputs from the flow diagram: 11, 7, 2, 5.

• For input 11: $11 \times 5 - 4 = 55 - 4 = 51$
• For input 7: $7 \times 5 - 4 = 35 - 4 = 31$
• For input 2: $2 \times 5 - 4 = 10 - 4 = 6$
• For input 5: $5 \times 5 - 4 = 25 - 4 = 21$ The output values are $\boxed{\text{51, 31, 6, 21}}$.

vi. What will the output values be if the rule is $+2 \times 7$?
This rule means to multiply the input by 7, then add 2. We will use the original inputs from the flow diagram: 11, 7, 2, 5.

• For input 11: $11 \times 7 + 2 = 77 + 2 = 79$
• For input 7: $7 \times 7 + 2 = 49 + 2 = 51$
• For input 2: $2 \times 7 + 2 = 14 + 2 = 16$
• For input 5: $5 \times 7 + 2 = 35 + 2 = 37$ The output values are $\boxed{\text{79, 51, 16, 37}}$.