Chapter 6.1, Problem 47SR

To determine

To graph: The solution of the inequality $18\le 12-2n$ on the number line.

Answer to Problem 47SR

The solution of given inequality is n≤-3 i.e. the set of all real numbers less than or equal to 3 that on number line is represented as:

  

Explanation of Solution

Given information: The inequality $18\le 12-2n$hat to be solved for variable n .

Concept used: To solve given inequality for n , subtract 12 each side. Then divide each side by 2 and then multiply each side by $-1$ and flip the inequality sign.

Calculation: On subtracting 12 each side,

  $\begin{array}{l}18-12\le -2n\\ \Rightarrow 6\le -2n\end{array}$

On dividing each side by 2,

  $\frac{6}{2}\le -n$

On multiplying each side by $-1$ and flipping the inequality sign

  $n\le -3$

Conclusion: So, n has all the real values less than or equal to $-3$ that can be shown on number line as :