Question

solve the inequality and graph the solution.
5 < 4(c + 8) - 11
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: Simplify the right - hand side

First, expand \(4(c + 8)-11\) using the distributive property \(a(b + c)=ab+ac\).
\(4(c + 8)-11=4c+32 - 11=4c + 21\).
So the inequality becomes \(5<4c + 21\).

Step2: Isolate the term with \(c\)

Subtract 21 from both sides of the inequality.
\(5-21<4c+21 - 21\).
\(-16<4c\).

Step3: Solve for \(c\)

Divide both sides of the inequality by 4.
\(\frac{-16}{4}<\frac{4c}{4}\).
\(- 4

Answer:

The solution of the inequality is \(c>-4\). On the number - line, we plot an open circle at \(c = - 4\) (because the inequality is strict, i.e., \(c
eq - 4\)) and draw a ray to the right of \(c=-4\).