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Solve Linear Equation Calculator

Solve ax + b = 0 for x.

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Solution x

Formula first

Overview

A linear equation is an algebraic equation of the first degree, representing a straight line when plotted on a coordinate plane. To isolate the variable x, one must perform inverse operations by subtracting the constant term and dividing by the lead coefficient, provided that the coefficient is non-zero.

Symbols

Variables

a = Coefficient a, b = Constant b, x = Solution x

Coefficient a
Variable
Constant b
Variable
Solution x
Variable

Apply it well

When To Use

When to use: This formula is used to find the root or x-intercept of a linear function. It is applicable whenever a relationship between two quantities can be expressed as a constant rate of change plus a starting value.

Why it matters: Linear equations are the building blocks of mathematics, used to model everything from financial budgeting to velocity in physics. Mastering this simple rearrangement is essential for solving more complex polynomial and differential equations.

Avoid these traps

Common Mistakes

  • Dividing by b instead of a.
  • Sign errors when moving b.

One free problem

Practice Problem

Practice Problem 1

Given the equation 5x + 25 = 0, solve for the unknown variable x.

Coefficient a5
Constant b25

Solve for:

Hint: Subtract the constant 25 from both sides before dividing by the coefficient 5.

Practice Problem 2

A line crosses the horizontal axis at a point described by 2x - 8 = 0. Find the value of x.

Coefficient a2
Constant b-8

Solve for:

Hint: Since b is -8, adding it to both sides will make it positive on the right side.

Practice Problem 3

Determine the value of x that satisfies the linear relationship 0.5x + 1 = 0.

Coefficient a0.5
Constant b1

Solve for:

Hint: Dividing a number by 0.5 is mathematically equivalent to multiplying that number by 2.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Wikipedia: Linear equation
  2. Britannica: Linear equation
  3. Stewart, James. Calculus: Early Transcendentals.
  4. Halliday, Resnick, and Walker, Fundamentals of Physics.
  5. Linear equation, Wikipedia
  6. Britannica, The Editors of Encyclopaedia. 'Linear equation'. Encyclopedia Britannica, 26 Oct. 2023.
  7. Stewart, James. Calculus: Early Transcendentals. Cengage Learning.
  8. AQA GCSE Maths — Algebra