Chapter 3, Problem 4CR

To determine

To check and explain:whether $-2x>6$ and $x>-3$ are equivalent inequalities.

Answer to Problem 4CR

$-2x>6$ and $x>-3$ are not an equivalent inequality.

Explanation of Solution

Given information:

The inequalities are:

  $-2x>6$ and $x>-3$

  $\begin{array}{l}-2x>6\text{ (Write the original inequality)}\\ \frac{-2x}{-2}>\frac{6}{-2}\text{ (Multiply each side by }-2.\text{ Reverse inequality symbol)}\\ x<-3\text{ (Simplify)}\end{array}$

From above solution it can be observed that $-2x>6$ and $x>-3$ is not an equivalent inequality.

Hence,

  $-2x>6$ and $x>-3$ is not an equivalent inequality.