Two Step Inequalities Practice

A two-step inequality is an inequality that requires two operations to isolate the variable. It typically involves addition or subtraction followed by multiplication or division.

First, subtract 5 from both sides: $$\frac{x}{2} \ge 5$$ . Then, multiply both sides by 2: $$x \ge 10$$ .

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.

First, subtract 10 from both sides: $$2.5x > 25$$ . Then, divide by 2.5: $$x > 10$$ .

The first step is to add 4 to both sides: $$3x < 15$$ .

An inequality has no solution if the variable cannot satisfy the inequality for any value. For example, $$x < x$$ is always false.

To check your solution, substitute a value from the solution set back into the original inequality to see if it holds true.

Subtract 3 from both sides: $$x > 4$$ . The solution set is all numbers greater than 4.

An equation states that two expressions are equal, while an inequality shows that one expression is greater than, less than, or not equal to another.

A compound inequality combines two inequalities, often using 'and' or 'or'. For example, $$x > 2 \text{ and } x < 5$$ .