Inequality symbols describe the relative size of two quantities when they are not necessarily equal. The main symbols are:
- $$\neq$$: not equal to
- $$<$$: less than
- $$\le$$: less than or equal to
- $$>$$: greater than
- $$\ge$$: greater than or equal to

Claude

On the number line, numbers get larger as they go from left to right. This spatial relationship can be used to explain the inequality symbols $$<$$ and $$>$$. If $$a$$ is to the left of $$b$$ on the number line, then $$a < b$$. If $$a$$ is to the right of $$b$$, then $$a > b$$.

Number Line and Inequalities

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OpenStax Intermediate Algebra

The expressions $$a < b$$ or $$a > b$$ can be read from left to right or right to left. In general, an inequality can be reversed as long as the symbol is flipped. Specifically, $$a < b$$ is equivalent to $$b > a$$, and $$a > b$$ is equivalent to $$b < a$$. For example, $$7 < 11$$ is equivalent to $$11 > 7$$.

Equivalent Inequalities

Inequality Symbols

The solution set of a one-variable linear inequality can be visually represented on a number line by shading the region that contains all satisfying values. The boundary value serves as the starting point of this solution set. To specify whether this boundary point is included, specific grouping symbols are employed: a square bracket $$[$$ is used for non-strict inequalities ($$\leq$$ or $$\geq$$) to show the boundary is part of the solution, while an open parenthesis $$($$ is used for strict inequalities ($$ < $$ or $$ > $$) to show the boundary is excluded. The number line is shaded to the right for 'greater than' solutions ($$ > $$, $$\geq$$) and to the left for 'less than' solutions ($$ < $$, $$\leq$$). For example, the inequality $$x > 3$$ has a solution set of any number strictly greater than $$3$$, so its graph features an open parenthesis at $$3$$ and shading extending to the right.

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