Definition: A two-step inequality is solved like a two-step equation, but you must reverse the inequality symbol whenever you multiply or divide both sides by a negative number.
What is a two-step inequality?
It compares expressions that need two inverse operations, like 3x – 4 < 11 or -2n + 5 >= 15.
How do you solve it?
Use the same steps as for an equation, then keep track of the symbol.
Solve 3x – 4 < 11. Add 4: 3x < 15. Divide by 3: x < 5. Any number less than 5 works.
What changes with negatives?
When you multiply or divide by a negative, flip the symbol. Solve -2n + 5 >= 15. Subtract 5: -2n >= 10. Divide by -2 and flip: n <= -5. Test n = -6: -2(-6) + 5 = 17, which is at least 15.
How do you graph it?
Use an open circle for < or >, a closed circle for <= or >=, and shade toward the solutions.
What is a common mistake?
Forgetting to flip. A quick check with a test value catches it. Using n = 0 in the last example gives 5 >= 15, which is false, so 0 must not be in the solution.