Linear Inequality Calculator

Linear Inequality Formula

Worked Example

The inequality −3x + 4 < 10:

1. −3x + 4 < 10
2. Subtract 4: −3x < 6
3. Divide by -3 (negative, so the sign flips): x > -2

Boundary (decimal): -2

Test-day tip

For word problems (“at most”, “at least”), write the inequality first, then check one value from the answer range in the original statement. On the SAT, graphing y = ax + b and y = c shows the solution as the x-values where one line is below the other.

More Algebra Calculators

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  a₁x + b₁y = c₁, a₂x + b₂y = c₂

  solved by elimination / Cramer’s rule; determinant 0 means no unique solution

  Example: The system 2x + 3y = 12 and x − y = 1: Solution: x = 3, y = 2.

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• Absolute Value Equation Calculator

  |ax + b| = c ⇔ ax + b = c or ax + b = −c

  no solution when c < 0; one solution when c = 0

  Example: The equation |2x − 3| = 7: Solutions: x = -2 or x = 5.

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• Slope Calculator

  m = (y₂ − y₁) ÷ (x₂ − x₁)

  rise over run between points (x₁, y₁) and (x₂, y₂)

  Example: The line through (1, 2) and (4, 8): Slope m = 2.

  Open the slope calculator →

• Slope-Intercept Form Calculator

  y = mx + b

  m slope, b y-intercept = y₁ − m·x₁

  Example: The line through (1, 2) and (4, 8): Slope-intercept form: y = 2x.

  Open the slope-intercept form calculator →

Frequently asked questions

Sources

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.