Inequality Solver
Solve linear inequalities like −2x + 3 ≥ 11, with the answer in interval notation.
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Solution
- Interval notation
- Steps
- Sign flipped?
- Work
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How to Solve a Linear Inequality
Solve it like an equation, with one rule: when you multiply or divide both sides by a negative number, reverse the inequality sign.
ax + b ≥ c → x ≥ (c − b) ÷ a if a > 0, x ≤ (c − b) ÷ a if a < 0
Parentheses mean the endpoint isn’t included (<, >); brackets mean it is (≤, ≥). On the number line, an open circle marks an excluded endpoint and a filled circle an included one.
Worked Example
Tips
Check with a test value: x = −5 gives −2(−5) + 3 = 13 ≥ 11, true.