Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '<' mean?

Back

The symbol '<' means 'less than'. For example, 3 < 5 means 3 is less than 5.

Front

What does the symbol '>' mean?

Back

The symbol '>' means 'greater than'. For example, 7 > 4 means 7 is greater than 4.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 5 means x can be less than or equal to 5.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. For example, y ≥ 2 means y can be greater than or equal to 2.

Front

How do you solve the inequality -3 < 2x - 1 < 5?

Back

Add 1 to all parts: -2 < 2x < 6. Then divide by 2: -1 < x < 3.

Front

What is a compound inequality?

Back

A compound inequality combines two inequalities, such as a < x < b, indicating that x is between a and b.

Front

How do you graph an inequality?

Back

To graph an inequality, use a number line and draw an open circle for < or >, and a closed circle for ≤ or ≥.

Front

What does |x| ≥ a mean?

Back

The expression |x| ≥ a means that x is either greater than or equal to a or less than or equal to -a.

Front

How do you solve the inequality -4a < 2(a + 12)?

Back

Distribute: -4a < 2a + 24. Add 4a to both sides: 0 < 6a + 24. Then isolate a: a > -4.