How to Solve Inequalities in One Variable

An inequality is a statement in which there is an expression on both sides connected by one of the following inequality symbols: less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). The solution set is usually represented by an infinite solution set.

Difficulty: Moderately Challenging

Instructions

How to Solve Inequalities in One Variable

1. Add up all the numbers on the left side of the inequality.

2. Add up all the numbers on the right side of the inequality.

3. Add up the variable with coefficients (i.e. 3x+4x) on the left side of the inequality.

4. Add up the variable with coefficients (i.e. 2x+x) on the right side of the inequality.

5. Subract the number on the left side (if it is a positive number) from both sides of the inequality or add the number on the left side (if it is a negative number) from both sides of the inequality.

6. Subract the variable with a coefficient on the right side of the inequality (if it is a positive variable with a coefficient ) from both sides of the inequality or add the variable with a coefficient on the right side of the inequality (if it is a negative variable with a coefficient) from both sides of the inequality.

7. Simplify (if needed) by dividing (if the coefficient is an integer) both sides of the inequality by the coefficient (i.e. the 8 in 8x) or multiplying both sides of the inequality by the reciprocal of the coefficient (if the coefficient is a fraction). Note: The inequality sign is reversed if both sides of the inequality are multiplied or divided by a negative number.

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