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 in inequalities?

Back

'>' means 'greater than'. For example, x > 5 means x is any number greater than 5.

Front

What does the symbol '<' mean in inequalities?

Back

'<'' means 'less than'. For example, x < 3 means x is any number less than 3.

Front

What does the symbol '≥' mean in inequalities?

Back

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

Front

What does the symbol '≤' mean in inequalities?

Back

'≤' means 'less than or equal to'. For example, x ≤ 2 means x is any number less than or equal to 2.

Front

How do you solve the inequality x + 9 > 21?

Back

Subtract 9 from both sides: x > 12.

Front

What is the solution to the inequality 5x + 5 - 4x - 8 ≤ 10?

Back

Combine like terms: x - 3 ≤ 10, then x ≤ 13.

Front

How do you solve the inequality 2(2x + 6) - 7 > 25?

Back

Distribute: 4x + 12 - 7 > 25, then 4x + 5 > 25, so 4x > 20, thus x > 5.

Front

What is the solution to the inequality -2x + 3(-4x + 6) ≤ 116?

Back

Distribute: -2x - 12x + 18 ≤ 116, combine like terms: -14x ≤ 98, thus x ≥ -7.

Front

How do you solve the inequality 15 + 7x ≥ 29?

Back

Subtract 15 from both sides: 7x ≥ 14, then divide by 7: x ≥ 2.