Question

graph the following inequalities:

1. -6 ≥ y
2. m < 7
3. -3 ≤ p

circle each inequality the symbol flips in when solving or graphing:

1. \\( \frac { y } { - 4 } \leq 5 \\)
2. 2b ≥ -8
3. x + 8 < -9
4. -10 > c + 4

solve and graph the following inequalities:

1. \\( \frac { x } { - 6 } > - 4 \\)
2. -7 + c < -9
3. t? or f? 5 is a solution to -3 + h ≥ 8

Explanation:

Step1: Solve the inequality \( \frac{x}{-6}>-4 \)

Multiply both sides by \(-6\). Remember to reverse the inequality sign when multiplying by a negative number.
\(x < (-4)\times(-6)\)
\(x < 24\)

Step2: Solve the inequality \( -7 + c<-9 \)

Add \(7\) to both sides.
\(c<-9 + 7\)
\(c<-2\)

Step3: Solve the inequality \( -3+h\geq8 \)

Add \(3\) to both sides.
\(h\geq8 + 3\)
\(h\geq11\)

Step4: Check if \(5\) is a solution to \( -3+h\geq8 \)

Substitute \(h = 5\) into the inequality: \(-3+5=2\). Since \(2<8\), \(5\) is not a solution.

Answer:

1. \(x < 24\)
2. \(c<-2\)
3. \(h\geq11\)
4. \(5\) is not a solution to \( -3 + h\geq8\)