Question

1. select all of the inequalities that have the value $n = -7$ as a solution.

$16 > -3n - 5$
$-3 < -7 - 2n$
$4 < 3n + 10$
$-2 > \frac{n}{7} - 8$

Explanation:

Step1: Test $n=-7$ in first inequality

Substitute $n=-7$ into $16 > -3n - 5$:
$16 > -3(-7) - 5 = 21 - 5 = 16$
$16 > 16$ is false.

Step2: Test $n=-7$ in second inequality

Substitute $n=-7$ into $-3 < -7 - 2n$:
$-3 < -7 - 2(-7) = -7 + 14 = 7$
$-3 < 7$ is true.

Step3: Test $n=-7$ in third inequality

Substitute $n=-7$ into $4 < 3n + 10$:
$4 < 3(-7) + 10 = -21 + 10 = -11$
$4 < -11$ is false.

Step4: Test $n=-7$ in fourth inequality

Substitute $n=-7$ into $-2 > \frac{n}{7} - 8$:
$-2 > \frac{-7}{7} - 8 = -1 - 8 = -9$
$-2 > -9$ is true.

Answer:

• $-3 < -7 - 2n$
• $-2 > \frac{n}{7} - 8$