Solving equations is a fundamental skill in algebra. It involves finding the value(s) for the variable(s) that make the equation true. The steps to solve an equation depend on the type of equation and can range from simple arithmetic to more complex algebraic manipulations.
Basic Steps for Solving Equations
- Simplify Both Sides: If necessary, simplify each side of the equation by combining like terms and distributing.
- Isolate the Variable: Use addition, subtraction, multiplication, and division to get the variable on one side of the equation and the numbers on the other.
- Check Your Solution: Substitute your solution back into the original equation to verify that it makes the equation true.
Example 1: Solving a Linear Equation
Solve the equation: 2x + 3 = 7.
First, isolate x: 2x = 7 – 3, so 2x = 4. Then, divide both sides by 2: x = 4 / 2, so x = 2.
The solution is x = 2.
Example 2: Solving a Quadratic Equation
Solve the equation: x^2 – 5x + 6 = 0.
First, factor the equation: (x – 2)(x – 3) = 0. Then, set each factor equal to zero: x – 2 = 0 or x – 3 = 0.
Solve each equation: x = 2 or x = 3.
The solutions are x = 2 and x = 3.
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