Question

solve the inequality and graph the solution.
2(v - 5) < -8
plot the endpoints. select an endpoint to change it from closed to open. select the middle of
the segment, ray, or line to delete it.

Explanation:

Step1: Expand the left - hand side

Use the distributive property \(a(b - c)=ab - ac\). Here \(a = 2\), \(b=v\), \(c = 5\).
\(2(v-5)=2v-10\). So the inequality becomes \(2v - 10\lt-8\).

Step2: Add 10 to both sides

To isolate the term with \(v\), use the addition property of inequalities.
\(2v-10 + 10\lt-8 + 10\).
Simplify to get \(2v\lt2\).

Step3: Divide both sides by 2

Use the division property of inequalities.
\(\frac{2v}{2}\lt\frac{2}{2}\).
Simplify to get \(v\lt1\).

Answer:

The solution of the inequality \(2(v - 5)\lt-8\) is \(v\lt1\). On the number - line, we have an open circle at \(v = 1\) (since the inequality is strict, \(v
eq1\)) and the ray extends to the left (towards the negative infinity).