1.5 Equations
Ideas in this lesson
- Is it a solution?
- Linear equations
- Solving for a variable
- Solving quadratics by factoring
- Completing the square
- The quadratic formula
- The discriminant
- Rational and radical equations
- Quadratic-type, power and absolute value equations
- Applications of supplied equations
Is it a solution? · Worked example
Which operation is guaranteed to preserve exactly the solution set of \(x(x-3)=0\)?
Answer: Subtract \(x(x-3)\) from both sides.
Adding or subtracting the same defined expression is reversible.
The original solutions are \(0\) and \(3\).
Dividing by \(x\) would discard \(x=0\).
Dividing by \(x-3\) would discard \(x=3\).
The original solutions are \(0\) and \(3\).
Dividing by \(x\) would discard \(x=0\).
Dividing by \(x-3\) would discard \(x=3\).