Two-Step Inequalities

Solving two-step inequalities is very similar to solving two-step equations. The goal is still to isolate the variable, but you need to be very careful with one specific rule related to inequalities.

The 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 two-step inequalities. Scroll down the page for more examples and solutions.

Algebra Worksheets
Practice your skills with the following Algebra worksheets:
Printable & Online Algebra Worksheets

Steps to solve a two-step inequality:

1. Identify the Operations
   Look for:
   Addition/Subtraction (solve first)
   Multiplication/Division (solve second)
   

2. Solve in Reverse PEMDAS Order
   Undo addition/subtraction (does not affect inequality sign).
   Undo multiplication/division (flip sign if dividing/multiplying by a negative).
   

3. Graph the Solution
   Open circle (○) for < or >
   Closed circle (●) for ≤ or ≥
   

Example 1: No Flipping Needed (Positive coefficient)
Solve: 2x + 5 < 11

1. Undo Addition: Subtract 5 from both sides.
   2x + 5 - 5 < 11 - 5
   2x < 6
   
2. Undo Multiplication: Divide both sides by 2
   \(\frac{2x}{2} < \frac{6}{2}\)
   x < 3
   

Example 2: Flipping Needed (Negative coefficient)
Solve: -3y - 4 ≥ 8

1. Undo Subtraction: Add 4 to both sides.
   -3y - 4 + 4 ≥ 8 + 4
   -3y ≥ 12
   
2. Undo Multiplication: Divide both sides by -3 (remember to flip the symbol)
   \(\frac{-3y}{-3} \le \frac{12}{-3} \)
   y ≤ -4
   

Two-step Inequality Example
This is a two-step inequality problem.

• Show Step-by-step Solutions

Two-step Inequality Example
This is an example of a two-step inequality problem.

• Show Step-by-step Solutions

Solve a Two Step Linear Inequality (Variable Left)
This video provides two examples of solving two step linear inequalities in one variable with the variable on the left. The solutions are also written using interval notation.

• Show Step-by-step Solutions

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