Chapter 5, Problem 1MCQ

To determine

To solve the inequality:

  $x-8>4$

And to graph the solution on a number line.

Answer to Problem 1MCQ

  $\left(12,\infty \right)$

  

Explanation of Solution

Given:

  $n+2\le -5,\text{ and }n+6\ge -6$

Concept Used:

• To graph the endpoint with strict inequality $<\text{ or}>$, use the open parenthesis or a hollow circle at that endpoint.
• To graph the endpoint with inequality symbol $\le \text{ or}\ge$, use the bracket or a solid circle at that endpoint.
• Properties of inequality:

1. $b\le c\Rightarrow b\pm a\le c\pm a$
2. $b\le c\Rightarrow ab\le ac,\text{ if }a>0$
3. $b\le c\Rightarrow ab\ge ac,\text{ if }a<0$

Calculation:

In order to solve the inequality:

  $x-8>4$

Add 8 both sides of the inequality, as

  $\begin{array}{c}x-8>4\\ \Rightarrow x-8+8>4+8\\ \Rightarrow x-0>12\\ \Rightarrow x>12\end{array}$

Thus, the solution of given inequality is every number strictly greater than 12, this can be represented in interval form, as

  $\left(12,\infty \right)$

Now, in order to sketch the graph of the solution of the inequality, since the interval of solution at left end point 12 is strict, so use a hollow circle at point 12. And the solution interval at right endpoint $\infty$ , thus every point greater than 12 is in the solution interval of given inequality. The graph of the solution of inequality is shown below: