Google Calculator for Algebra

Linear Equation Solver (ax + b = c)

Coefficient 'a':

Constant 'b':

Constant 'c':

Understanding Linear Equations and How to Solve Them

A linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line. The most common form for a single-variable linear equation is ax + b = c, where 'x' is the variable, and 'a', 'b', and 'c' are constants.

Components of a Linear Equation:

'x' (Variable): This is the unknown value we aim to find.
'a' (Coefficient): This number multiplies the variable 'x'. If 'a' is 0, the equation is no longer truly linear in 'x'.
'b' (Constant Term): This is a fixed number added to the 'ax' term on the left side of the equation.
'c' (Constant Term): This is a fixed number on the right side of the equation.

How to Solve `ax + b = c`:

The goal is to isolate 'x' on one side of the equation. Here are the steps:

Subtract 'b' from both sides: This moves the constant 'b' from the left side to the right side.
ax + b - b = c - b
ax = c - b
Divide both sides by 'a': This isolates 'x'.
ax / a = (c - b) / a
x = (c - b) / a

Special Cases:

If 'a' is 0:
- If 0x = 0 (meaning c - b = 0), then there are infinitely many solutions, as any value of 'x' will satisfy the equation.
- If 0x = (a non-zero number) (meaning c - b ≠ 0), then there is no solution, as 0 multiplied by any number can never equal a non-zero number.

Using the Calculator:

Our Linear Equation Solver helps you quickly find the value of 'x' for equations in the form ax + b = c. Simply input the values for 'a', 'b', and 'c' into the respective fields, and the calculator will apply the algebraic steps to determine 'x'.

Examples:

Let's look at a few examples:

Example 1: Simple Solution

Equation: 2x + 5 = 15
Input 'a': 2
Input 'b': 5
Input 'c': 15
Calculation: x = (15 - 5) / 2 = 10 / 2 = 5
Result: x = 5

Example 2: Negative Numbers

Equation: -3x + 7 = 1
Input 'a': -3
Input 'b': 7
Input 'c': 1
Calculation: x = (1 - 7) / -3 = -6 / -3 = 2
Result: x = 2

Example 3: No Solution

Equation: 0x + 4 = 9
Input 'a': 0
Input 'b': 4
Input 'c': 9
Calculation: 0x = 9 - 4 => 0x = 5. This is impossible.
Result: No Solution

Example 4: Infinite Solutions

Equation: 0x + 6 = 6
Input 'a': 0
Input 'b': 6
Input 'c': 6
Calculation: 0x = 6 - 6 => 0x = 0. Any 'x' works.
Result: Infinite Solutions

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