Chapter 6.2, Problem 48E

To determine

Tosolve: the inequality.

Answer to Problem 48E

  $x\ge 2\frac{3}{4}$

Explanation of Solution

Given information: consider the expression provided in the question,

  $-\frac{2}{5}x+\frac{6}{5}\ge \frac{1}{10}$

Calculation:

Subtract $\frac{6}{5}$ from both sides,

  $\begin{array}{l}-\frac{2}{5}x+\frac{6}{5}-\frac{6}{5}\ge \frac{1}{10}-\frac{6}{5}\\ -\frac{2}{5}x\ge \frac{1-12}{10}\\ -\frac{2}{5}x\ge -\frac{11}{10}\\ \frac{2}{5}x\ge \frac{11}{10}\end{array}$

Multiply the multiplicative inverse of $\frac{2}{5}$ on both sides,

  $\begin{array}{l}\frac{2}{5}x·\frac{5}{2}\ge \frac{11}{10}·\frac{5}{2}\\ x\ge \frac{11}{4}\\ x\ge 2\frac{3}{4}\end{array}$

Hence, the quotient of the expression is $x\ge 2\frac{3}{4}$