Inequalities and Absolute Value Equations

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '>' represent in inequalities?

Back

The symbol '>' means 'greater than'. For example, x > 4 means x is any number greater than 4.

Front

What does the symbol '<' represent in inequalities?

Back

The symbol '<' means 'less than'. For example, x < 8 means x is any number less than 8.

Front

How do you solve the inequality 3x - 10 > 2?

Back

Add 10 to both sides: 3x > 12. Then divide by 3: x > 4.

Front

What is the solution to the inequality x + 5 ≤ 13?

Back

Subtract 5 from both sides: x ≤ 8.

Front

How do you solve the inequality 8x < 48?

Back

Divide both sides by 8: x < 6.

Front

What inequality does the number line graph represent if it shows all values less than -4?

Back

x < -4.

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

Front

Back

Set up two equations: x + 10 = 11 and x + 10 = -11. Solve to get x = 1 and x = -21.

Front

What does the symbol '≥' mean in inequalities?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 4 means x is 4 or any number greater than 4.