Find the solution of the inequality.

Understand the Problem

The question appears to be asking for the solution to an inequality involving the expressions presented. It may involve determining the sign of the expressions given certain conditions.

Answer

The solution is $(-\infty, -1) \cup (1, 4)$.

Steps to Solve

Identify the Inequalities We have four inequalities:

$x < -1$
$x < 4$
$x > 1$
$x > 1$ (duplicate)

Determine the Overall Range To find the solution set, we analyze the individual inequalities:

From $x < -1$, we have one part of the solution where $x$ can take values less than -1.
From $x < 4$, we have values less than 4.
From $x > 1$, we have values greater than 1.

Combine the Inequalities Now we combine these results. The intervals can be summarized as follows:

The solution for $x < -1$ is $(-\infty, -1)$.
The solution for $x > 1$ is $(1, \infty)$.

Final Solution Thus, the overall solution to the given inequalities can be expressed as: $$ (-\infty, -1) \cup (1, 4) $$

These intervals reflect all possible $x$ that satisfy at least one of the given inequalities.

The solution to the inequality is: $$ (-\infty, -1) \cup (1, 4) $$

More Information

This solution shows all the values of $x$ that satisfy at least one of the inequalities. The interval notation means that $x$ can take any value less than -1 or between 1 and 4.

Tips

A common mistake is to incorrectly combine the inequalities, leading to an inaccurate range.
Not recognizing that $x > 1$ is relevant and should not simply be ignored.

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