Equations and Inequalities

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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.

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What does the symbol '≥' mean?

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The symbol '≥' means 'greater than or equal to'.

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What does the symbol '≤' mean?

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The symbol '≤' means 'less than or equal to'.

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Back

First, isolate x: 5 - 2 \ge \frac{x}{-3} \Rightarrow 3 \ge \frac{x}{-3} \Rightarrow 3 \times -3 \le x \Rightarrow -9 \le x. The solution is -9 ≤ x.

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To solve for x, divide both sides by 2: x = 2.

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Add 9 to both sides: n \ge 14. The solution is n ≥ 14.

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Subtract 4 from both sides: -2x < 12. Divide by -2 (remember to flip the inequality): x > -6.

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Subtract 1 from both sides: 2x = 8. Divide by 2: x = 4.

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What is a closed dot on a number line?

Back

A closed dot indicates that the number is included in the solution set (e.g., x ≤ -9).

Front

What is an open dot on a number line?

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An open dot indicates that the number is not included in the solution set (e.g., x > -6).