Math - Inequalities

Inequalities are mathematical expressions that compare values using the following symbols:

• >: Greater than
• <: Less than
• ≥: Greater than or equal to
• ≤: Less than or equal to

Unlike equations, which express equality, inequalities show a relationship where one value is not necessarily equal to another.

Inverting Inequality Operators

When multiplying or dividing both sides of an inequality by a negative number, you must reverse the inequality symbol:

• > becomes <;
• ≥ becomes ≤;
• < becomes >;
• ≤ becomes ≥;

Example

$-2x > 6\\ -2x * -1 > 6 * -1\\ 2x < -6$

Solving Simple Inequalities

To solve inequalities, it’s similar to solving equations.

Addition Inequality

$x + 4 > 12\\ x + 4 - 4 > 12 - 4\\ x > 8$

Subtraction Inequality

$x - 7 < 2\\ x - 7 + 7 < 2 + 7\\ x < 9$

Multiplication Inequality

$3x \ge 12\\ \frac{\cancel{3}x}{\cancel{3}} \ge \frac{12}{3}\\ x \ge 4$

Division Inequality

$\frac{x}{2} \le 3\\ 2 * \frac{x}{2} \le 3 * 2\\ \cancel{2} * \frac{x}{\cancel{2}} \le 6\\ x \le 6$