Inequalities
This Grade 6 algebra skill from Yoshiwara Elementary Algebra introduces inequalities in one variable. Students learn to write, solve, and graph inequalities such as x > 3 or 2x ≤ 8 on a number line, and understand that an inequality has infinitely many solutions unlike a single-answer equation.
Key Concepts
Property A statement that uses one of the symbols $ $ or $<$ is called an inequality . An inequality that uses the symbol for less than, $<$, or greater than, $ $, is called a strict inequality . A nonstrict inequality uses one of the following symbols: $\geq$ means "greater than or equal to"; $\leq$ means "less than or equal to".
Examples The inequality $x 5$ represents all numbers strictly greater than 5. On a number line, this is shown with an open circle at 5 and an arrow pointing to the right. The inequality $y \leq 2$ represents 2 and all numbers less than it. On a number line, this is shown with a solid dot at 2 and an arrow pointing to the left. The values 8, 9.5, and 200 all satisfy the inequality $x \geq 8$, but 7.9 does not.
Explanation Inequalities describe a range of possible values, not just a single answer. A strict inequality ($<$ or $ $) uses an open circle on a number line, while a non strict one ($\leq$ or $\geq$) uses a solid dot to show the endpoint is included.
Common Questions
What is an inequality in algebra?
An inequality is a mathematical statement comparing two expressions using symbols like > (greater than), < (less than), ≥, or ≤. For example, x > 5.
How do you solve a linear inequality?
Use the same steps as solving an equation—apply inverse operations to isolate the variable. Remember: when multiplying or dividing by a negative number, reverse the inequality sign.
How do you graph an inequality on a number line?
Use an open circle for strict inequalities (< or >) and a closed circle for inclusive ones (≤ or ≥), then shade the appropriate direction.
How many solutions does an inequality have?
An inequality has infinitely many solutions. For example, x > 3 is satisfied by 4, 5, 3.1, 3.001, and every number greater than 3.
Where are inequalities introduced in Grade 6?
Inequalities are introduced in the Yoshiwara Elementary Algebra textbook for Grade 6.