Absolute Value Equation Calculator
An absolute value equation splits into two linear equations: |2x − 3| = 7 has x = -2 or x = 5.
x = -2 or x = 5
- x₁ (decimal)
- -2
- x₂ (decimal)
- 5
Step-by-step solution
- |2x − 3| = 7 splits into 2x − 3 = 7 or 2x − 3 = -7
- x = (7 − (-3)) ÷ 2 = 5
- x = (-7 − (-3)) ÷ 2 = -2
Absolute Value Equation Formula
|ax + b| = c ⇔ ax + b = c or ax + b = −c
no solution when c < 0; one solution when c = 0
Worked Example
The equation |2x − 3| = 7:
- |2x − 3| = 7 splits into 2x − 3 = 7 or 2x − 3 = -7
- x = (7 − (-3)) ÷ 2 = 5
- x = (-7 − (-3)) ÷ 2 = -2
x₂ (decimal): 5
Test-day tip
Graph y = |2x − 3| and y = 7 in the SAT graphing calculator: the solutions are the x-coordinates where the V-shape crosses the horizontal line.
More Algebra Calculators
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ax + b < c → x < (c − b)/a
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Example: The inequality −3x + 4 < 10: Solution = x > -2.
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m = (y₂ − y₁) ÷ (x₂ − x₁)
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Example: The line through (1, 2) and (4, 8): Slope m = 2.
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Slope-Intercept Form Calculator
y = mx + b
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Example: The line through (1, 2) and (4, 8): Slope-intercept form: y = 2x.
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Point-Slope Form Calculator
y − y₁ = m(x − x₁)
point (x₁, y₁), slope m
Example: The line through (1, 2) with slope 3: Point-slope form: y − 2 = 3(x − 1).
Frequently asked questions
Why can |ax + b| = −5 have no solution?
An absolute value is a distance, so it is never negative. Any equation setting it equal to a negative number has no solution.
What is the sum of the solutions of |ax + b| = c?
The two solutions are symmetric about x = −b/a, so they add up to −2b/a. For |2x − 3| = 7 the sum is 3.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Absolute Value Equation Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/absolute-value-equation-calculator/
IEEE
Scientific Converters, "Absolute Value Equation Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/absolute-value-equation-calculator/