Math

Absolute Value Equation Calculator

An absolute value can never equal a negative number, so c < 0 gives no real solution.

Solve |ax + b| = c for both solutions.

Calculated Output

Solution x₁ 8

Solution x₂ -2

Formula: ax + b = ±c ⟹ x = (±c − b) ÷ a

Step-by-Step Breakdown

1. Values used:

2. a = 1

3. b = -3

4. c = 5

6. Solution x₁ = 8

7. Solution x₂ = a + b = 1 + -3 = -2

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The math behind it

|ax + b| = c means ax + b = c OR ax + b = −c. Solve each for x. If c < 0 there is no solution; if c = 0 the two solutions coincide.

|x − 3| = 5 → x − 3 = 5 (x = 8) or x − 3 = −5 (x = −2).

Why can it have no solution?

An absolute value can never equal a negative number, so c < 0 gives no real solution.