Solving inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, ≥) to show that one expression is not equal to the other.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that a value can be either less than or equal to a specified number.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that a value can be either greater than or equal to a specified number.

Front

How do you solve the inequality 3x + 5 + 2x > 35?

Back

Combine like terms: 5x + 5 > 35. Then subtract 5 from both sides: 5x > 30. Finally, divide by 5: x > 6.

Front

What is the solution to the inequality x/4 - 9 ≤ 3?

Back

Add 9 to both sides: x/4 ≤ 12. Then multiply both sides by 4: x ≤ 48.

Front

How do you express 'at most 10' in inequality form?

Back

'At most 10' can be expressed as x ≤ 10.

Front

How do you express 'at least 15' in inequality form?

Back

'At least 15' can be expressed as x ≥ 15.

Front

What is the solution to the inequality 2x + 6 > 12?

Back

Subtract 6 from both sides: 2x > 6. Then divide by 2: x > 3.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary value, while non-strict inequalities (≤, ≥) do include the boundary value.

Front

How do you graph the inequality x < 10?

Back

Draw a number line, place an open circle at 10, and shade to the left to indicate all numbers less than 10.