Question

solve for n and graph the solution.
10 ≤ -19n - 4 + 17n < 14
plot the endpoints. select an endpoint to change it from closed to open. select the middle of a segment, ray, or line to delete it.

Explanation:

Step1: Combine like terms

$10 \leq -2n - 4 < 14$

Step2: Add 4 to all parts

$10 + 4 \leq -2n - 4 + 4 < 14 + 4$
$14 \leq -2n < 18$

Step3: Divide by -2, reverse inequalities

$\frac{14}{-2} \geq n > \frac{18}{-2}$
$-7 \geq n > -9$

Answer:

The solution is $-9 < n \leq -7$.

For the graph:

• Plot an open circle at $n=-9$ (since the inequality is strict, $n > -9$)
• Plot a closed circle at $n=-7$ (since the inequality is non-strict, $n \leq -7$)
• Draw a line segment connecting these two points to represent all values between -9 and -7, including -7 but not including -9.