Solving Inequalities

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 '<' mean?

Back

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

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What does the symbol '>' mean?

Back

The symbol '>' means 'greater than'. For example, x > 3 means x is greater than 3.

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What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 4 means x is less than or equal to 4.

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What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 2 means x is greater than or equal to 2.

Front

How do you solve the inequality -4 + y < -8?

Back

To solve -4 + y < -8, add 4 to both sides: y < -4.

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How do you solve the inequality x + 5 > 7?

Back

To solve x + 5 > 7, subtract 5 from both sides: x > 2.

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What is the solution to the inequality -9x + 7 ≥ 25?

Back

To solve -9x + 7 ≥ 25, subtract 7 from both sides and then divide by -9: x ≤ -2.

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What does it mean if a graph shows a closed circle on a number line?

Back

A closed circle indicates that the number is included in the solution set, meaning the inequality is 'greater than or equal to' (≥) or 'less than or equal to' (≤).

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What does it mean if a graph shows an open circle on a number line?

Back

An open circle indicates that the number is not included in the solution set, meaning the inequality is 'greater than' (>) or 'less than' (<).