Answer
If $x$ is negative, we change "less than" symbol with "more than".
$x>3$
If $x$ is positive, the symbol stays the same.
$x<3$
Solution:
$\left\{ \begin{array}{ll} x>3 & \quad if & \quad x∈(-\infty, 0) \\ x<3 & \quad if & \quad x ∈ (0, +\infty) \end{array} \right. $
Work Step by Step
We cannot simply multiply an inequality as we do for an equation. While multiplying an inequality to any real number, we have to consider whether the number is positive or negative.
When we multiply by negative number we have to reverse the inequality (Change $$ and vice versa). In this case, we cannot multiply by $x$ as we don't know the sign of $x$.
We have to consider two possible solution if we multiply by $x$.
We have original inequality $1 \frac {3\times x}{x}$
$x>3$
If $x$ is positive, the symbol stays the same.
$1\times x < \frac{3\times x}{x}$
$x<3$
Solution:
$\left\{ \begin{array}{ll} x>3 & \quad if & \quad x∈(-\infty, 0) \\ x<3 & \quad if & \quad x ∈ (0, +\infty) \end{array} \right. $
