An inequality is a mathematical expression that shows the relationship between two values when they are not necessarily equal. Unlike equations, which show that two expressions are equal, inequalities show that one expression is greater than or less than another.

The main inequality symbols are:

• > means "greater than" (e.g., 5 > 3)
• < means "less than" (e.g., 2 < 6)
• ≥ means "greater than or equal to" (e.g., 7 ≥ 5)
• ≤ means "less than or equal to" (e.g., 3 ≤ 4)
• ≠ means "not equal to" (e.g., 4 ≠ 5)

To solve inequalities, follow similar steps as solving equations, but with some important differences. For example, when multiplying or dividing both sides of an inequality by a negative number, the inequality symbol flips (changes direction).

Examples:

Example 1: Solving a Simple Inequality
Solve: 2x + 3 > 7
Step 1: Subtract 3 from both sides.
2x > 7 - 3
2x > 4
Step 2: Divide both sides by 2.
x > 4 / 2
x > 2
So, the solution is x > 2. This means any value of x that is greater than 2 satisfies the inequality.

Example 2: Solving an Inequality with a Negative Number
Solve: -3x < 12
Step 1: Divide both sides by -3. Remember to flip the inequality symbol when dividing by a negative number!
x > -12 / 3
x > -4
So, the solution is x > -4. Any value of x that is greater than -4 satisfies the inequality.

Inequalities are useful in many real-world situations, such as finding possible values for a variable that satisfy certain conditions, like limits or ranges.

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