Inequality
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
In Algebra 1, an inequality is a mathematical statement that compares two expressions and shows the relationship between them in terms of their relative size. Here’s a detailed breakdown:
Definition: An inequality is a statement that indicates that one side of the inequality is either greater than, less than, greater than or equal to, or less than or equal to the other side. It describes a range of possible values rather than a single value.
Inequality Symbols:
Greater Than (>): Indicates that the value on the left is larger than the value on the right. Example: x > 5 means x is greater than 5.
Less Than (<): Indicates that the value on the left is smaller than the value on the right. Example: x < 3 means x is less than 3.
Greater Than or Equal To (>): Indicates that the value on the left is either greater than or equal to the value on the right. Example: x > 4 means x is greater than or equal to 4.
Less Than or Equal To (<): Indicates that the value on the left is either less than or equal to the value on the right. Example: x < 2 means x is less than or equal to 2.
Solving Inequalities:
Similar to Equations: To solve inequalities, you perform operations to isolate the variable, similar to solving equations. This may include adding, subtracting, multiplying, or dividing both sides of the inequality by the same number.
Multiplying/Dividing by Negative Numbers: When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign. For example, if you have -2x < 6 and divide both sides by -2, the inequality becomes x > -3.
Graphing Inequalities:
On a Number Line: Inequalities can be represented on a number line where you shade the appropriate region to show the set of values that satisfy the inequality. Use open or closed circles to indicate whether the boundary value is included or not.
Examples:
Inequality: 3x + 2 < 11
Solution: Subtract 2 from both sides to get 3x < 9, then divide by 3 to find x < 3. The solution set includes all values of x that are less than or equal to 3.
Inequality: x - 5 > 7
Solution: Add 5 to both sides to get x > 12. The solution set includes all values of x that are greater than 12.
In summary, an inequality is a statement that shows the relationship between two expressions in terms of their relative size and includes values that satisfy that relationship.