Algebra One Linear Equation Solver (ax + b = c)
Result:
Understanding Algebra One: Solving Linear Equations
Algebra One is a foundational branch of mathematics that introduces variables, equations, and the methods to solve them. One of the most common tasks in Algebra One is solving linear equations, which are equations where the highest power of the variable is one. Our calculator focuses on solving linear equations in the standard form: ax + b = c.
What is a Linear Equation?
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 general form we're using, ax + b = c, involves:
x: The variable you are trying to solve for.a: The coefficient ofx. This is a number that multipliesx.b: A constant term on the left side of the equation.c: A constant term on the right side of the equation.
The goal is to isolate x on one side of the equation to find its value.
How to Solve ax + b = c
The process involves two main steps:
- Isolate the
axterm: Subtractbfrom both sides of the equation.ax + b - b = c - bax = c - b - Isolate
x: Divide both sides bya(assumingais not zero).ax / a = (c - b) / ax = (c - b) / a
Using the Algebra One Linear Equation Solver
Our calculator simplifies this process for you. Simply input the values for a, b, and c from your equation, and it will instantly provide the value of x.
Examples:
Let's look at a few examples to illustrate how the calculator works:
Example 1: Basic Equation
Solve for x in the 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: Equation with Negative Numbers
Solve for x in the equation: -3x + 7 = -8
- Input 'a':
-3 - Input 'b':
7 - Input 'c':
-8 - Calculation:
x = (-8 - 7) / -3 = -15 / -3 = 5 - Result:
x = 5
Example 3: Equation with Zero Coefficient 'a'
Consider the equation: 0x + 4 = 4
- Input 'a':
0 - Input 'b':
4 - Input 'c':
4 - Result: "Infinitely many solutions." (Since
4 = 4is always true, any value ofxworks).
Example 4: Another Zero Coefficient 'a' Case
Consider the equation: 0x + 6 = 10
- Input 'a':
0 - Input 'b':
6 - Input 'c':
10 - Result: "No solution." (Since
6 = 10is false, no value ofxcan make the equation true).
Why is this important?
Solving linear equations is a fundamental skill in mathematics and is applied across various fields, including science, engineering, economics, and even daily problem-solving. It forms the basis for understanding more complex algebraic concepts and systems of equations.