Chapter 8.8, Problem 65CCR

To determine

Solve the inequality $14\ge 7+a$ and graph the solution on number line

Answer to Problem 65CCR

The solution of the inequality is $a\le 7$

The graph of the solution $a\le 7$ on number line is below:

  

Explanation of Solution

Given:

The inequality, $14\ge 7+a$

Concept used:

• If there is the strict inequality symbol $<\text{ or}>$ , then use a parenthesis $\left(\right)$ on the interval
• If there is the inequality symbol $\le \text{ or}\ge$ , then use a bracket $\left[\right]$ on the interval
• Inequality sign get reverse on multiplying or dividing by a negative number

Calculation:

• In order to solve the mixed inequality $14\ge 7+a$ first isolate the variable term a by performing some basic operations. Here to isolate a terms on the left side, first subtract both sides by $7$ and then simplify further as shown below:

  $\begin{array}{c}14\ge 7+a\\ 14-7\ge 7+a-7\\ 7\ge a\\ \Rightarrow a\le 7\end{array}$

Thus, the solution of the given inequality is $a\le 7$ .

The graph of the inequality solution $a\le 7$ is below: