Linear Inequality Solver
ax ≤ b → solve for x
Coefficient a (of x)
Inequality
Right-hand side b
✓Solution
x ≤ 5.0000
A linear inequality solver finds all values of x satisfying an inequality like 2x ≤ 10. Unlike equations with one solution, inequalities have a range of solutions, displayed as an interval.
- 1Solve like an equation, but flip inequality when multiplying/dividing by negative
- 22x ≤ 10 → x ≤ 5
- 3−3x > 6 → x < −2 (flip when dividing by −3)
- 4Represent solution as interval: (−∞, 5]
2x ≤ 10=x ≤ 5 (interval: (−∞, 5])
−3x > 6=x < −2 (interval: (−∞, −2))
| Symbol | Meaning | Interval notation | Number line |
|---|---|---|---|
| < | Less than | (a, b) | Open circle |
| ≤ | Less or equal | [a, b] | Closed circle |
| > | Greater than | (a, +∞) | Open circle |
| ≥ | Greater or equal | [a, +∞) | Closed circle |
References
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