Multi-Step Inequalities

Solving multi-step inequalities involves combining the techniques you use for solving multi-step equations. The goal remains the same: isolate the variable on one side of the inequality symbol.

Rule of Inequalities:
When you multiply or divide both sides of an inequality by a negative number, you MUST reverse (flip) the direction of the inequality symbol.

The following figure shows how to solve multi-step inequalities. Scroll down the page for more examples and solutions.

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Steps to Solve Multi-Step Inequalities:

1. Clear Parentheses: If there are parentheses, distribute any numbers outside them.
   
2. Combine Like Terms: Combine like terms on each side of the inequality separately.
   
3. Collect Variable Terms: Get all terms containing the variable on one side of the inequality and all constant terms on the other side.
   It’s often helpful to move the variable term to the side where its coefficient will end up positive, if possible, to avoid needing to flip the inequality sign later.
   
4. Isolate the Variable: Perform multiplication or division to isolate the variable.
   Remember to flip the inequality symbol if you multiply or divide by a negative number.
   
5. Simplify: Perform any final arithmetic.
   
6. Check (Optional but Recommended): Pick a value from your solution set and plug it into the original inequality to ensure it makes the inequality true. Pick a value outside the solution set and ensure it makes the inequality false.

Solving Multi-Step Inequalities
How to solve multi-step inequalities?
Examples:

1. 15 - 10r < 24
   
2. -b/2 + 9 ≥ -3
   
3. 1.8x - 3.4 > 5.6
   
4. 12(m - 4) ≤ 3m - 3
   
5. 1/2 c - 1/4 ≤ -3/4
   
6. 10 < -8x - 6

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Multi-Step Inequalities

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Multi-Step Inequalities 2

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Solving Multi-Step Inequalities

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