An inequality, similar to an equation, is a mathematical statement comparing two quantities. Some inequalities indicate that the two quantities are not necessarily equal, while others are strictly never equal.
|Symbol||Meaning||Strict / Non-strict|
|is less than||Strict|
|≤||is less than or equal to||Non-strict|
|is greater than||Strict|
|≥||is greater than or equal to||Non-strict|
If a value is a solution to an inequality, it is an element of the solution set. To determine if r=2 is a solution, we can substitute the value into the inequality and evaluate. If the resulting inequality is true, the value is a solution; if it's false, it is not a solution.
The graph of a one-variable inequality is a visual representation of the inequality's solution set, which can be drawn on a number line in three steps:
An arrow in either direction indicates that all numbers in that direction are part of the solution set.
Graph the inequality x<9 on a number line.
The inequality reads is less than which means that x=9 is not a solution to the inequality, but every value of x less than 9 is. Thus, our graph must have an open circle at x=9.
Every value of x less than 9 also has to be included in the graph. Since smaller numbers lie to the left on the number line, this is graphed as an arrow pointing to the left.
We have now fully graphed the inequality x<9.
Write the inequality shown by the graph.