Inequalities and Intervals
\pi \cdot \pi
\pi \cdot \pi
Types of Inequalities
Less than
In inequalities, use \(<\)
In graphs, use \(\circ\)
In intervals, use parenthesis ( )
\pi \cdot \pi
Types of Inequalities
\(x<5\)
\pi \cdot \pi
Types of Inequalities
\(x<5\)
5
\pi \cdot \pi
Types of Inequalities
\(x<5\)
5
\pi \cdot \pi
Types of Inequalities
\(x<5\)
5
\pi \cdot \pi
Types of Inequalities
\(x<5\)
5
\((-\infty,5)\)
\pi \cdot \pi
Types of Inequalities
Greater than
In inequalities, use \(>\)
In graphs, use \(\circ\)
In intervals, use parenthesis ( )
\pi \cdot \pi
Types of Inequalities
\(x>5\)
\pi \cdot \pi
Types of Inequalities
\(x>5\)
5
\pi \cdot \pi
Types of Inequalities
\(x>5\)
5
\pi \cdot \pi
Types of Inequalities
\(x>5\)
5
\pi \cdot \pi
Types of Inequalities
\(x>5\)
5
\((5, \infty)\)
\pi \cdot \pi
Types of Inequalities
Less than or equal to
In inequalities, use \(\leq\)
In graphs, use
⬤
In intervals, use brackets [ ]
\pi \cdot \pi
Types of Inequalities
\(x\leq5\)
\pi \cdot \pi
Types of Inequalities
\(x\leq5\)
5
\pi \cdot \pi
Types of Inequalities
\(x\leq5\)
5
\pi \cdot \pi
Types of Inequalities
\(x\leq5\)
5
\pi \cdot \pi
Types of Inequalities
\(x\leq5\)
5
\((-\infty,5]\)
\pi \cdot \pi
Types of Inequalities
Greater than or equal to
In inequalities, use \(\geq\)
In graphs, use
⬤
In intervals, use brackets [ ]
\pi \cdot \pi
Types of Inequalities
\(x\geq5\)
\pi \cdot \pi
Types of Inequalities
\(x\geq5\)
5
\pi \cdot \pi
Types of Inequalities
\(x\geq5\)
5
\pi \cdot \pi
Types of Inequalities
\(x\geq5\)
5
\pi \cdot \pi
Types of Inequalities
\(x\geq5\)
5
\([5, \infty)\)
\pi \cdot \pi
Dealing with Inequalities
Always make sure the variable is on the left side of the inequality.
Arrow goes in the direction of the inequality IF THE VARIABLE IS ON THE LEFT.
When reading a graph, you always read from left to right.
When writing an interval, always use parenthesis around \(-\infty\) and \(\infty\). The smaller number always goes on the left.
Include starts with I which looks like ][.