Question

solve the inequality and graph the solution.
16 ≥ 2(c - 4) + 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.
submit

Explanation:

Step1: Simplify the right - hand side

$$16\geq2(c - 4)+8$$
First, expand \(2(c - 4)\) using the distributive property \(a(b + c)=ab+ac\). Here \(a = 2\), \(b=c\), \(c=-4\), so \(2(c - 4)=2c-8\). Then the inequality becomes \(16\geq2c-8 + 8\). Simplify the right - hand side: \(2c-8 + 8=2c\), so \(16\geq2c\).

Step2: Solve for \(c\)

Divide both sides of the inequality \(16\geq2c\) by \(2\). Using the property \(\frac{a}{m}\geq\frac{b}{m}\) when \(m>0\) (here \(m = 2>0\)). We get \(\frac{16}{2}\geq\frac{2c}{2}\), which simplifies to \(8\geq c\) or \(c\leq8\).

Answer:

The solution of the inequality is \(c\leq8\). On the number - line, we have a closed circle at \(c = 8\) (since the inequality is \(\leq\), which includes the endpoint) and a ray extending to the left.