Question

examples 1, 3, and 4
solve each compound inequality. then graph the sol

1. $f - 6 < 5$ and $f - 4 \geq 2$
2. $y - 1 \geq 7$ or $y + 3 < -1$
3. $-5 < 3p + 7 \leq 22$
4. $5h - 4 \geq 6$ and $7h + 11 < 32$

examples 5 and 6
write a compound inequality that descr

Explanation:

Step1: Solve \(5h - 4\geq6\)

Add 4 to both sides: \(5h-4 + 4\geq6 + 4\)
Simplify: \(5h\geq10\)
Divide by 5: \(h\geq\frac{10}{5}=2\)

Step2: Solve \(7h + 11\lt32\)

Subtract 11: \(7h+11 - 11\lt32 - 11\)
Simplify: \(7h\lt21\)
Divide by 7: \(h\lt\frac{21}{7}=3\)

Step3: Find intersection

The solution to the compound inequality (and) is the overlap of \(h\geq2\) and \(h\lt3\), so \(2\leq h\lt3\)

Answer:

\(2\leq h\lt3\)