Question

1. when do you flip the inequality sign?

a. everytime you divide
b. always
c. when you multiply or divide by a negative
d. never (dont choose me)

1. solve the inequality and check for all possible solutions.

$-9 - 1y + 4 > 0$

Explanation:

For Question 13:

This is a conceptual question about inequality rules. The key rule is that the inequality sign is flipped only when multiplying or dividing both sides by a negative number.

Step1: Combine constant terms

$$\begin{align*} -9 + 4 - y &> 0 \\ -5 - y &> 0 \end{align*}$$

Step2: Isolate the variable term

$$\begin{align*} -y &> 0 + 5 \\ -y &> 5 \end{align*}$$

Step3: Multiply by -1, flip sign

$$\begin{align*} y &< -5 \end{align*}$$

Step4: Verify with test value

Test $y=-6$: $-9 - (-6) + 4 = -9 +6 +4 =1>0$, which is true.
Test $y=-5$: $-9 - (-5) +4 = -9+5+4=0$, which is not greater than 0.
Test $y=-4$: $-9 - (-4)+4 = -9+4+4=-1<0$, which is false.

Answer:

C. When you multiply or divide by a negative

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For Question 14: