Math - Inequalities

Inequalities in math are expressions that contain:

• '>' - greater than
• '<' - less than
• '$\ge$' - greater than or equal to
• '$\le$' - less than or equal to

Where the relationship between these two expressions is not equal (which is why it is not an equation).

Inverting Operators in Inequalities

Sometimes, you will need to reverse the inequality operator:

Example

-3x < 6

$-3x < 6\\ -3x \times -1 < 6 \times -1\\ 3x > -6\\ \frac{\cancel{3}x}{\cancel{3}} > \frac{-6}{3}\\ x > -2$

Solving Simple Inequalities

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

Addition Inequality

x + 4 > 12

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

Subtraction Inequality

x - 7 < 2

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

Multiplication Inequality

$3x \ge 12$

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

Division Inequality

$\frac{x}{2} \le 3$

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