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Solve The Following Linear Equation Calculator

Reviewed by Calculator Editorial Team

This calculator solves linear equations in the form ax + b = c. It finds the value of x by rearranging the equation to isolate x. The solution is displayed with a step-by-step explanation and visualized on a chart.

How to Use This Calculator

To solve a linear equation using this calculator:

  1. Enter the coefficient of x (a) in the first input field.
  2. Enter the constant term (b) in the second input field.
  3. Enter the right-hand side of the equation (c) in the third input field.
  4. Click the "Calculate" button to solve the equation.
  5. The solution will appear in the result box below with a step-by-step explanation.

The calculator will display the solution in the form x = (c - b)/a. If the equation has no solution or infinite solutions, it will indicate that.

Formula Explained

A linear equation in one variable has the general form:

ax + b = c

To solve for x, we rearrange the equation:

ax = c - b x = (c - b)/a

Where:

  • a is the coefficient of x
  • b is the constant term on the left side
  • c is the constant term on the right side

Note: The equation has a unique solution only when a ≠ 0. If a = 0, the equation either has no solution (if b ≠ c) or infinite solutions (if b = c).

Worked Examples

Example 1: Simple Linear Equation

Solve 3x + 2 = 11

  1. Identify a = 3, b = 2, c = 11
  2. Rearrange: 3x = 11 - 2 → 3x = 9
  3. Divide both sides by 3: x = 3

The solution is x = 3.

Example 2: Equation with Negative Numbers

Solve -2x + 5 = 1

  1. Identify a = -2, b = 5, c = 1
  2. Rearrange: -2x = 1 - 5 → -2x = -4
  3. Divide both sides by -2: x = 2

The solution is x = 2.

Example 3: Equation with No Solution

Solve 4x + 3 = 4x + 7

  1. Identify a = 4, b = 3, c = 7
  2. Rearrange: 4x - 4x + 3 = 7 → 3 = 7
  3. This is a contradiction, so there is no solution.

The equation has no solution.

Frequently Asked Questions

What is a linear equation?

A linear equation is an equation that produces a straight line when graphed. It has the general form ax + b = c, where a, b, and c are constants.

How do I solve a linear equation?

To solve a linear equation, isolate the variable by performing inverse operations. For ax + b = c, subtract b from both sides and then divide by a.

What if the coefficient of x is zero?

If a = 0, the equation becomes b = c. If b = c, there are infinitely many solutions. If b ≠ c, there is no solution.