Question

circle each inequality the symbol flips in when solving or graphing:
solve and graph the following inequalities:

1. $\frac{y}{-4}\leq5$
2. $2b\geq - 8$
3. $x + 8 < - 9$
4. $-10>c + - 4$
5. $\frac{x}{-6}>-4$
6. $-7 + c < - 9$
7. t? or f? 5 is a solution to $-3 + h\geq8$

Explanation:

Step1: Solve inequality \( \frac{y}{-4}\leq5 \)

Multiply both sides by \(-4\). When multiplying by a negative number, the inequality sign flips. So \( y\geq - 20 \).

Step2: Solve inequality \( 2b\geq - 8 \)

Divide both sides by \(2\). The inequality sign remains the same. So \( b\geq - 4 \).

Step3: Solve inequality \( x + 8\lt - 9 \)

Subtract \(8\) from both sides. The inequality sign remains the same. So \( x\lt - 17 \).

Step4: Solve inequality \( - 10\gt c + 4 \)

Subtract \(4\) from both sides. The inequality sign remains the same. So \( c\lt - 14 \).

Step5: Solve inequality \( \frac{x}{-6}\gt - 4 \)

Multiply both sides by \(-6\). When multiplying by a negative number, the inequality sign flips. So \( x\lt24 \).

Step6: Solve inequality \( - 7 + c\lt - 9 \)

Add \(7\) to both sides. The inequality sign remains the same. So \( c\lt - 2 \).

Step7: Solve inequality \( - 3+h\geq8 \)

Add \(3\) to both sides. The inequality sign remains the same. So \( h\geq11 \).

Step8: Check if \(5\) is a solution to \( - 3+h\geq8 \)

Substitute \(h = 5\) into \( - 3+h\). We get \( - 3 + 5=2\). Since \(2\lt8\), \(5\) is not a solution. So the answer is \(F\) (False).

Answer:

1. \( y\geq - 20 \); 5. \( b\geq - 4 \); 6. \( x\lt - 17 \); 7. \( c\lt - 14 \); 8. \( x\lt24 \); 9. \( c\lt - 2 \); 10. \(F\) (False)