Chapter 3.2, Problem 41PPE

To determine

To find:

Solution of the inequality $\frac{3}{5}+d\ge -\frac{2}{5}$ . To graph it and to check its solutions.

Answer to Problem 41PPE

Solution of the given inequality in interval form is $d=[-1,\infty )$ that is shown red in below graph:

  

Explanation of Solution

Given information:

Inequality $\frac{3}{5}+d\ge -\frac{2}{5}$ is given.

Concept used:

Get the solution of given inequality by removing all terms, associated with unknown variable. Do just opposite operation of that term, each side to eliminate its term.

Calculation:

Subtract $\frac{3}{5}$ each side in given inequality,

  $\begin{array}{l}\frac{3}{5}-\frac{3}{5}+d\ge -\frac{2}{5}-\frac{3}{5}\\ \Rightarrow d\ge -\frac{5}{5}\\ \Rightarrow d\ge -1\end{array}$

On number line, show this solution as:

  

Check: Substitute a value from above solution set, say, $d=0$ in given inequality,

  $\begin{array}{l}\frac{3}{5}+0\ge -\frac{2}{5}\\ \Rightarrow \frac{3}{5}\ge -\frac{2}{5}\end{array}$

that is true, so given solution set is correct.

Conclusion:

So, solution of the given inequality is the set of all the real values, those are greater or equal to, $-1$ , as shown in above graph also.