Strict Inequality — Definition, Meaning & Examples
Worked Example
Problem: Solve the strict inequality 2x + 1 > 7 and describe its solution set.
Step 1: Subtract 1 from both sides.
2x>6
Step 2: Divide both sides by 2.
x>3
Step 3: Because this is a strict inequality, x = 3 is NOT included in the solution set. In interval notation, the solution is written with a parenthesis (open endpoint), not a bracket.
x∈(3,∞)
Answer: The solution is all real numbers greater than 3, not including 3 itself: x∈(3,∞).
Why It Matters
The distinction between strict and non-strict inequalities determines whether boundary values are included in a solution set. When graphing on a number line, a strict inequality uses an open circle to show the endpoint is excluded, while a non-strict inequality uses a closed circle. This same idea carries into graphing linear inequalities, where strict inequalities produce dashed boundary lines rather than solid ones.
Common Mistakes
Mistake: Including the boundary value in the solution set. For example, writing x≥3 or using a closed circle at 3 when the inequality is x>3.
Correction: With a strict inequality, the boundary value is never a solution. Use an open circle on the number line and a parenthesis in interval notation to show exclusion.
Related Terms
- Inequality — General category that includes strict and non-strict
- Non-Strict Inequality — Uses ≤ or ≥, allowing equality at the boundary
- Greater Than — One of the two strict inequality symbols
- Less Than — The other strict inequality symbol
- Interval Notation — Uses parentheses for strict inequality endpoints