Question

solve the inequality and graph the solution. 2(n + 14) ≤ 20. 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

Expand \(2(n + 14)\) using the distributive property \(a(b + c)=ab+ac\). Here \(a = 2\), \(b=n\) and \(c = 14\), so \(2(n + 14)=2n+28\). The inequality becomes \(2n + 28\leq20\).

Step2: Isolate the variable term

Subtract 28 from both sides of the inequality \(2n+28\leq20\). We get \(2n+28 - 28\leq20 - 28\), which simplifies to \(2n\leq - 8\).

Step3: Solve for \(n\)

Divide both sides of the inequality \(2n\leq - 8\) by 2. Since \(2>0\), the direction of the inequality sign remains the same. So \(\frac{2n}{2}\leq\frac{-8}{2}\), which gives \(n\leq - 4\).

Step4: Graph the solution

On the number - line, plot a closed circle at \(n=-4\) (because the inequality is \(\leq\)) and draw a ray to the left of \(n = - 4\) to represent all the values of \(n\) that satisfy the inequality.

Answer:

The solution of the inequality \(2(n + 14)\leq20\) is \(n\leq - 4\). On the number - line, plot a closed circle at \(-4\) and draw a ray to the left.