Equation Solver Calculator
Solution
Solution will appear here
Step-by-Step Solution
Original equation: \(2x + 5 = 13\)
We start with the given equation.
Subtract 5 from both sides: \(2x = 8\)
Isolate the variable term by subtracting 5.
Divide both sides by 2: \(x = 4\)
Solve for x by dividing both sides by 2.
System Solution
x = 2
Variable 1
y = 1
Variable 2
Solution Steps
Equation 1: \(2x + 3y = 7\)
Equation 2: \(x - y = 1\)
We'll solve this system using substitution.
From Equation 2: \(x = y + 1\)
Solve Equation 2 for x.
Substitute into Equation 1: \(2(y + 1) + 3y = 7\)
Replace x with (y + 1) in Equation 1.
Inequality Solution
Solution: x ≥ 4
Solution Steps
Original inequality: \(2x - 3 ≥ 5\)
We start with the given inequality.
Add 3 to both sides: \(2x ≥ 8\)
Isolate the variable term.
Divide both sides by 2: \(x ≥ 4\)
Solve for x, maintaining the inequality direction.
Understanding Equation Solving
Equation solving is fundamental to algebra and mathematics. Here's what you need to know:
- Linear Equations: Equations of the form ax + b = c. Solution is x = (c - b)/a
- Quadratic Equations: Equations of the form ax² + bx + c = 0. Solved using quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
- Complex Solutions: When discriminant is negative, solutions involve imaginary numbers
- Systems of Equations: Multiple equations solved simultaneously using substitution, elimination, or matrix methods
Equation Solving Tips
Consider these tips for solving equations:
- Always perform the same operation on both sides of the equation
- Combine like terms to simplify equations before solving
- For quadratic equations, calculate the discriminant first
- When solving inequalities, remember to flip the sign when multiplying/dividing by negative numbers
- Check your solutions by plugging them back into the original equation
Supported Equation Types
Our calculator can solve:
- Linear equations: 2x + 5 = 13
- Quadratic equations: x² - 5x + 6 = 0
- Systems of equations (2 or 3 variables)
- Inequalities: 2x - 3 ≥ 5
- Absolute value equations: |x - 4| = 2
- Equations with parameters: solve ax + b = c for x
- Trigonometric identities: sin²x + cos²x = 1
About Step-by-Step Solutions
Our calculator shows each step of the solution process:
- Initial equation parsing and simplification
- Isolating variable terms
- Performing operations to solve for the variable
- Checking for extraneous solutions
- Graphical representation when applicable